Search

Cultural accumulation drives the open-ended and diverse progress in capabilities spanning human history. It builds an expanding body of knowledge and skills by combining individual exploration with inter-generational information transmission. Despite its widespread success among humans, the capacity for artificial learning agents to accumulate culture remains under-explored. In particular, approaches to reinforcement learning typically strive for improvements over only a single lifetime. Generational algorithms that do exist fail to capture the open-ended, emergent nature of cultural accumulation, which allows individuals to trade-off innovation and imitation. Building on the previously demonstrated ability for reinforcement learning agents to perform social learning, we find that training setups which balance this with independent learning give rise to cultural accumulation. These accumulating agents outperform those trained for a single lifetime with the same cumulative experience. We explore this accumulation by constructing two models under two distinct notions of a generation: episodic generations, in which accumulation occurs via in-context learning and train-time generations, in which accumulation occurs via in-weights learning. In-context and in-weights cultural accumulation can be interpreted as analogous to knowledge and skill accumulation, respectively. To the best of our knowledge, this work is the first to present general models that achieve emergent cultural accumulation in reinforcement learning, opening up new avenues towards more open-ended learning systems, as well as presenting new opportunities for modelling human culture.

Traditionally, cognitive and computer scientists have viewed intelligence solipsistically, as a property of unitary agents devoid of social context. Given the success of contemporary learning algorithms, we argue that the bottleneck in artificial intelligence (AI) progress is shifting from data assimilation to novel data generation. We bring together evidence showing that natural intelligence emerges at multiple scales in networks of interacting agents via collective living, social relationships and major evolutionary transitions, which contribute to novel data generation through mechanisms such as population pressures, arms races, Machiavellian selection, social learning and cumulative culture. Many breakthroughs in AI exploit some of these processes, from multi-agent structures enabling algorithms to master complex games like Capture-The-Flag and StarCraft II, to strategic communication in Diplomacy and the shaping of AI data streams by other AIs. Moving beyond a solipsistic view of agency to integrate these mechanisms suggests a path to human-like compounding innovation through ongoing novel data generation., Comment: 17 pages, 2 figures, 1 box

Normal-form games with two players, each with two strategies, are the most studied class of games. These so-called 2x2 games are used to model a variety of strategic interactions. They appear in game theory, economics, and artificial intelligence research. However, there lacks tools for describing and visualizing such games. This work introduces a LaTeX package for visualizing 2x2 games. This work has two goals: first, to provide high-quality tools and vector graphic visualizations, suitable for scientific publications. And second, to help promote standardization of names and representations of 2x2 games. The LaTeX package, twoxtwogame, is maintained on GitHub and mirrored on CTAN, and is available under a permissive Apache 2 license.

We study computationally efficient methods for finding equilibria in n-player general-sum games, specifically ones that afford complex visuomotor skills. We show how existing methods would struggle in this setting, either computationally or in theory. We then introduce NeuPL-JPSRO, a neural population learning algorithm that benefits from transfer learning of skills and converges to a Coarse Correlated Equilibrium (CCE) of the game. We show empirical convergence in a suite of OpenSpiel games, validated rigorously by exact game solvers. We then deploy NeuPL-JPSRO to complex domains, where our approach enables adaptive coordination in a MuJoCo control domain and skill transfer in capture-the-flag. Our work shows that equilibrium convergent population learning can be implemented at scale and in generality, paving the way towards solving real-world games between heterogeneous players with mixed motives.

Cooperation in multi-agent learning (MAL) is a topic at the intersection of numerous disciplines, including game theory, economics, social sciences, and evolutionary biology. Research in this area aims to understand both how agents can coordinate effectively when goals are aligned and how they may cooperate in settings where gains from working together are possible but possibilities for conflict abound. In this paper we provide an overview of the fundamental concepts, problem settings and algorithms of multi-agent learning. This encompasses reinforcement learning, multi-agent sequential decision-making, challenges associated with multi-agent cooperation, and a comprehensive review of recent progress, along with an evaluation of relevant metrics. Finally we discuss open challenges in the field with the aim of inspiring new avenues for research., Comment: 29 pages, 3 figures

Agent-based modeling has been around for decades, and applied widely across the social and natural sciences. The scope of this research method is now poised to grow dramatically as it absorbs the new affordances provided by Large Language Models (LLM)s. Generative Agent-Based Models (GABM) are not just classic Agent-Based Models (ABM)s where the agents talk to one another. Rather, GABMs are constructed using an LLM to apply common sense to situations, act "reasonably", recall common semantic knowledge, produce API calls to control digital technologies like apps, and communicate both within the simulation and to researchers viewing it from the outside. Here we present Concordia, a library to facilitate constructing and working with GABMs. Concordia makes it easy to construct language-mediated simulations of physically- or digitally-grounded environments. Concordia agents produce their behavior using a flexible component system which mediates between two fundamental operations: LLM calls and associative memory retrieval. A special agent called the Game Master (GM), which was inspired by tabletop role-playing games, is responsible for simulating the environment where the agents interact. Agents take actions by describing what they want to do in natural language. The GM then translates their actions into appropriate implementations. In a simulated physical world, the GM checks the physical plausibility of agent actions and describes their effects. In digital environments simulating technologies such as apps and services, the GM may handle API calls to integrate with external tools such as general AI assistants (e.g., Bard, ChatGPT), and digital apps (e.g., Calendar, Email, Search, etc.). Concordia was designed to support a wide array of applications both in scientific research and for evaluating performance of real digital services by simulating users and/or generating synthetic data., Comment: 32 pages, 5 figures

The ability of humans to create and disseminate culture is often credited as the single most important factor of our success as a species. In this Perspective, we explore the notion of machine culture, culture mediated or generated by machines. We argue that intelligent machines simultaneously transform the cultural evolutionary processes of variation, transmission, and selection. Recommender algorithms are altering social learning dynamics. Chatbots are forming a new mode of cultural transmission, serving as cultural models. Furthermore, intelligent machines are evolving as contributors in generating cultural traits--from game strategies and visual art to scientific results. We provide a conceptual framework for studying the present and anticipated future impact of machines on cultural evolution, and present a research agenda for the study of machine culture.

Social dilemmas present a significant challenge in multi-agent cooperation because individuals are incentivised to behave in ways that undermine socially optimal outcomes. Consequently, self-interested agents often avoid collective behaviour. In response, we formalise social dilemmas and introduce a novel metric, the general self-interest level, to quantify the disparity between individual and group rationality in such scenarios. This metric represents the maximum proportion of their individual rewards that agents can retain while ensuring that a social welfare optimum becomes a dominant strategy. Our approach diverges from traditional concepts of altruism, instead focusing on strategic reward redistribution. By transferring rewards among agents in a manner that aligns individual and group incentives, rational agents will maximise collective welfare while pursuing their own interests. We provide an algorithm to compute efficient transfer structures for an arbitrary number of agents, and introduce novel multi-player social dilemma games to illustrate the effectiveness of our method. This work provides both a descriptive tool for analysing social dilemmas and a prescriptive solution for resolving them via efficient reward transfer contracts. Applications include mechanism design, where we can assess the impact on collaborative behaviour of modifications to models of environments., Comment: 35 pages, 15 tables, 2 figures. Submitted to the Journal of Autonomous Agents and Multi-Agent Systems: Special Issue on Citizen-Centric AI Systems

Today, using Large-scale generative Language Models (LLMs) it is possible to simulate free responses to interview questions like those traditionally analyzed using qualitative research methods. Qualitative methodology encompasses a broad family of techniques involving manual analysis of open-ended interviews or conversations conducted freely in natural language. Here we consider whether artificial "silicon participants" generated by LLMs may be productively studied using qualitative methods aiming to produce insights that could generalize to real human populations. The key concept in our analysis is algorithmic fidelity, a term introduced by Argyle et al. (2023) capturing the degree to which LLM-generated outputs mirror human sub-populations' beliefs and attitudes. By definition, high algorithmic fidelity suggests latent beliefs elicited from LLMs may generalize to real humans, whereas low algorithmic fidelity renders such research invalid. Here we used an LLM to generate interviews with silicon participants matching specific demographic characteristics one-for-one with a set of human participants. Using framework-based qualitative analysis, we showed the key themes obtained from both human and silicon participants were strikingly similar. However, when we analyzed the structure and tone of the interviews we found even more striking differences. We also found evidence of the hyper-accuracy distortion described by Aher et al. (2023). We conclude that the LLM we tested (GPT-3.5) does not have sufficient algorithmic fidelity to expect research on it to generalize to human populations. However, the rapid pace of LLM research makes it plausible this could change in the future. Thus we stress the need to establish epistemic norms now around how to assess validity of LLM-based qualitative research, especially concerning the need to ensure representation of heterogeneous lived experiences., Comment: 52 pages, 5 tables, 5 figures

Is it possible to evaluate the moral cognition of complex artificial agents? In this work, we take a look at one aspect of morality: `doing the right thing for the right reasons.' We propose a behavior-based analysis of artificial moral cognition which could also be applied to humans to facilitate like-for-like comparison. Morally-motivated behavior should persist despite mounting cost; by measuring an agent's sensitivity to this cost, we gain deeper insight into underlying motivations. We apply this evaluation to a particular set of deep reinforcement learning agents, trained by memory-based meta-reinforcement learning. Our results indicate that agents trained with a reward function that includes other-regarding preferences perform helping behavior in a way that is less sensitive to increasing cost than agents trained with more self-interested preferences., Comment: 11 pages, 3 figures

In social psychology, Social Value Orientation (SVO) describes an individual's propensity to allocate resources between themself and others. In reinforcement learning, SVO has been instantiated as an intrinsic motivation that remaps an agent's rewards based on particular target distributions of group reward. Prior studies show that groups of agents endowed with heterogeneous SVO learn diverse policies in settings that resemble the incentive structure of Prisoner's dilemma. Our work extends this body of results and demonstrates that (1) heterogeneous SVO leads to meaningfully diverse policies across a range of incentive structures in sequential social dilemmas, as measured by task-specific diversity metrics; and (2) learning a best response to such policy diversity leads to better zero-shot generalization in some situations. We show that these best-response agents learn policies that are conditioned on their co-players, which we posit is the reason for improved zero-shot generalization results.

Many environments contain numerous available niches of variable value, each associated with a different local optimum in the space of behaviors (policy space). In such situations it is often difficult to design a learning process capable of evading distraction by poor local optima long enough to stumble upon the best available niche. In this work we propose a generic reinforcement learning (RL) algorithm that performs better than baseline deep Q-learning algorithms in such environments with multiple variably-valued niches. The algorithm we propose consists of two parts: an agent architecture and a learning rule. The agent architecture contains multiple sub-policies. The learning rule is inspired by fitness sharing in evolutionary computation and applied in reinforcement learning using Value-Decomposition-Networks in a novel manner for a single-agent's internal population. It can concretely be understood as adding an extra loss term where one policy's experience is also used to update all the other policies in a manner that decreases their value estimates for the visited states. In particular, when one sub-policy visits a particular state frequently this decreases the value predicted for other sub-policies for going to that state. Further, we introduce an artificial chemistry inspired platform where it is easy to create tasks with multiple rewarding strategies utilizing different resources (i.e. multiple niches). We show that agents trained this way can escape poor-but-attractive local optima to instead converge to harder-to-discover higher value strategies in both the artificial chemistry environments and in simpler illustrative environments., Comment: Full length paper accompanying short format appearing at AAMAS 2023

Multi-agent artificial intelligence research promises a path to develop intelligent technologies that are more human-like and more human-compatible than those produced by "solipsistic" approaches, which do not consider interactions between agents. Melting Pot is a research tool developed to facilitate work on multi-agent artificial intelligence, and provides an evaluation protocol that measures generalization to novel social partners in a set of canonical test scenarios. Each scenario pairs a physical environment (a "substrate") with a reference set of co-players (a "background population"), to create a social situation with substantial interdependence between the individuals involved. For instance, some scenarios were inspired by institutional-economics-based accounts of natural resource management and public-good-provision dilemmas. Others were inspired by considerations from evolutionary biology, game theory, and artificial life. Melting Pot aims to cover a maximally diverse set of interdependencies and incentives. It includes the commonly-studied extreme cases of perfectly-competitive (zero-sum) motivations and perfectly-cooperative (shared-reward) motivations, but does not stop with them. As in real-life, a clear majority of scenarios in Melting Pot have mixed incentives. They are neither purely competitive nor purely cooperative and thus demand successful agents be able to navigate the resulting ambiguity. Here we describe Melting Pot 2.0, which revises and expands on Melting Pot. We also introduce support for scenarios with asymmetric roles, and explain how to integrate them into the evaluation protocol. This report also contains: (1) details of all substrates and scenarios; (2) a complete description of all baseline algorithms and results. Our intention is for it to serve as a reference for researchers using Melting Pot 2.0., Comment: 69 pages, 54 figures. arXiv admin note: text overlap with arXiv:2107.06857

Human ecological success relies on our characteristic ability to flexibly self-organize into cooperative social groups, the most successful of which employ substantial specialization and division of labor. Unlike most other animals, humans learn by trial and error during their lives what role to take on. However, when some critical roles are more attractive than others, and individuals are self-interested, then there is a social dilemma: each individual would prefer others take on the critical but unremunerative roles so they may remain free to take one that pays better. But disaster occurs if all act thusly and a critical role goes unfilled. In such situations learning an optimum role distribution may not be possible. Consequently, a fundamental question is: how can division of labor emerge in groups of self-interested lifetime-learning individuals? Here we show that by introducing a model of social norms, which we regard as emergent patterns of decentralized social sanctioning, it becomes possible for groups of self-interested individuals to learn a productive division of labor involving all critical roles. Such social norms work by redistributing rewards within the population to disincentivize antisocial roles while incentivizing prosocial roles that do not intrinsically pay as well as others.

Advances in artificial intelligence often stem from the development of new environments that abstract real-world situations into a form where research can be done conveniently. This paper contributes such an environment based on ideas inspired by elementary Microeconomics. Agents learn to produce resources in a spatially complex world, trade them with one another, and consume those that they prefer. We show that the emergent production, consumption, and pricing behaviors respond to environmental conditions in the directions predicted by supply and demand shifts in Microeconomics. We also demonstrate settings where the agents' emergent prices for goods vary over space, reflecting the local abundance of goods. After the price disparities emerge, some agents then discover a niche of transporting goods between regions with different prevailing prices -- a profitable strategy because they can buy goods where they are cheap and sell them where they are expensive. Finally, in a series of ablation experiments, we investigate how choices in the environmental rewards, bartering actions, agent architecture, and ability to consume tradable goods can either aid or inhibit the emergence of this economic behavior. This work is part of the environment development branch of a research program that aims to build human-like artificial general intelligence through multi-agent interactions in simulated societies. By exploring which environment features are needed for the basic phenomena of elementary microeconomics to emerge automatically from learning, we arrive at an environment that differs from those studied in prior multi-agent reinforcement learning work along several dimensions. For example, the model incorporates heterogeneous tastes and physical abilities, and agents negotiate with one another as a grounded form of communication.

A key challenge in the study of multiagent cooperation is the need for individual agents not only to cooperate effectively, but to decide with whom to cooperate. This is particularly critical in situations when other agents have hidden, possibly misaligned motivations and goals. Social deduction games offer an avenue to study how individuals might learn to synthesize potentially unreliable information about others, and elucidate their true motivations. In this work, we present Hidden Agenda, a two-team social deduction game that provides a 2D environment for studying learning agents in scenarios of unknown team alignment. The environment admits a rich set of strategies for both teams. Reinforcement learning agents trained in Hidden Agenda show that agents can learn a variety of behaviors, including partnering and voting without need for communication in natural language.

Undesired bias afflicts both human and algorithmic decision making, and may be especially prevalent when information processing trade-offs incentivize the use of heuristics. One primary example is \textit{statistical discrimination} -- selecting social partners based not on their underlying attributes, but on readily perceptible characteristics that covary with their suitability for the task at hand. We present a theoretical model to examine how information processing influences statistical discrimination and test its predictions using multi-agent reinforcement learning with various agent architectures in a partner choice-based social dilemma. As predicted, statistical discrimination emerges in agent policies as a function of both the bias in the training population and of agent architecture. All agents showed substantial statistical discrimination, defaulting to using the readily available correlates instead of the outcome relevant features. We show that less discrimination emerges with agents that use recurrent neural networks, and when their training environment has less bias. However, all agent algorithms we tried still exhibited substantial bias after learning in biased training populations., Comment: 29 pages, 10 figures

Existing evaluation suites for multi-agent reinforcement learning (MARL) do not assess generalization to novel situations as their primary objective (unlike supervised-learning benchmarks). Our contribution, Melting Pot, is a MARL evaluation suite that fills this gap, and uses reinforcement learning to reduce the human labor required to create novel test scenarios. This works because one agent's behavior constitutes (part of) another agent's environment. To demonstrate scalability, we have created over 80 unique test scenarios covering a broad range of research topics such as social dilemmas, reciprocity, resource sharing, and task partitioning. We apply these test scenarios to standard MARL training algorithms, and demonstrate how Melting Pot reveals weaknesses not apparent from training performance alone., Comment: Accepted to ICML 2021 and presented as a long talk; 33 pages; 9 figures

Social learning, copying other's behavior without actual experience, offers a cost-effective means of knowledge acquisition. However, it raises the fundamental question of which individuals have reliable information: successful individuals versus the majority. The former and the latter are known respectively as success-based and conformist social learning strategies. We show here that while the success-based strategy fully exploits the benign environment of low uncertainly, it fails in uncertain environments. On the other hand, the conformist strategy can effectively mitigate this adverse effect. Based on these findings, we hypothesized that meta-control of individual and social learning strategies provides effective and sample-efficient learning in volatile and uncertain environments. Simulations on a set of environments with various levels of volatility and uncertainty confirmed our hypothesis. The results imply that meta-control of social learning affords agents the leverage to resolve environmental uncertainty with minimal exploration cost, by exploiting others' learning as an external knowledge base.

Society is characterized by the presence of a variety of social norms: collective patterns of sanctioning that can prevent miscoordination and free-riding. Inspired by this, we aim to construct learning dynamics where potentially beneficial social norms can emerge. Since social norms are underpinned by sanctioning, we introduce a training regime where agents can access all sanctioning events but learning is otherwise decentralized. This setting is technologically interesting because sanctioning events may be the only available public signal in decentralized multi-agent systems where reward or policy-sharing is infeasible or undesirable. To achieve collective action in this setting we construct an agent architecture containing a classifier module that categorizes observed behaviors as approved or disapproved, and a motivation to punish in accord with the group. We show that social norms emerge in multi-agent systems containing this agent and investigate the conditions under which this helps them achieve socially beneficial outcomes.

Collective action demands that individuals efficiently coordinate how much, where, and when to cooperate. Laboratory experiments have extensively explored the first part of this process, demonstrating that a variety of social-cognitive mechanisms influence how much individuals choose to invest in group efforts. However, experimental research has been unable to shed light on how social cognitive mechanisms contribute to the where and when of collective action. We build and test a computational model of human behavior in Clean Up, a social dilemma task popular in multi-agent reinforcement learning research. We show that human groups effectively cooperate in Clean Up when they can identify group members and track reputations over time, but fail to organize under conditions of anonymity. A multi-agent reinforcement learning model of reputation demonstrates the same difference in cooperation under conditions of identifiability and anonymity. In addition, the model accurately predicts spatial and temporal patterns of group behavior: in this public goods dilemma, the intrinsic motivation for reputation catalyzes the development of a non-territorial, turn-taking strategy to coordinate collective action.

Generalization is a major challenge for multi-agent reinforcement learning. How well does an agent perform when placed in novel environments and in interactions with new co-players? In this paper, we investigate and quantify the relationship between generalization and diversity in the multi-agent domain. Across the range of multi-agent environments considered here, procedurally generating training levels significantly improves agent performance on held-out levels. However, agent performance on the specific levels used in training sometimes declines as a result. To better understand the effects of co-player variation, our experiments introduce a new environment-agnostic measure of behavioral diversity. Results demonstrate that population size and intrinsic motivation are both effective methods of generating greater population diversity. In turn, training with a diverse set of co-players strengthens agent performance in some (but not all) cases., Comment: Accepted at Autonomous Agents and Multi-Agent Systems

The real world is awash with multi-agent problems that require collective action by self-interested agents, from the routing of packets across a computer network to the management of irrigation systems. Such systems have local incentives for individuals, whose behavior has an impact on the global outcome for the group. Given appropriate mechanisms describing agent interaction, groups may achieve socially beneficial outcomes, even in the face of short-term selfish incentives. In many cases, collective action problems possess an underlying graph structure, whose topology crucially determines the relationship between local decisions and emergent global effects. Such scenarios have received great attention through the lens of network games. However, this abstraction typically collapses important dimensions, such as geometry and time, relevant to the design of mechanisms promoting cooperation. In parallel work, multi-agent deep reinforcement learning has shown great promise in modelling the emergence of self-organized cooperation in complex gridworld domains. Here we apply this paradigm in graph-structured collective action problems. Using multi-agent deep reinforcement learning, we simulate an agent society for a variety of plausible mechanisms, finding clear transitions between different equilibria over time. We define analytic tools inspired by related literatures to measure the social outcomes, and use these to draw conclusions about the efficacy of different environmental interventions. Our methods have implications for mechanism design in both human and artificial agent systems., Comment: AAMAS 2021

Problems of cooperation--in which agents seek ways to jointly improve their welfare--are ubiquitous and important. They can be found at scales ranging from our daily routines--such as driving on highways, scheduling meetings, and working collaboratively--to our global challenges--such as peace, commerce, and pandemic preparedness. Arguably, the success of the human species is rooted in our ability to cooperate. Since machines powered by artificial intelligence are playing an ever greater role in our lives, it will be important to equip them with the capabilities necessary to cooperate and to foster cooperation. We see an opportunity for the field of artificial intelligence to explicitly focus effort on this class of problems, which we term Cooperative AI. The objective of this research would be to study the many aspects of the problems of cooperation and to innovate in AI to contribute to solving these problems. Central goals include building machine agents with the capabilities needed for cooperation, building tools to foster cooperation in populations of (machine and/or human) agents, and otherwise conducting AI research for insight relevant to problems of cooperation. This research integrates ongoing work on multi-agent systems, game theory and social choice, human-machine interaction and alignment, natural-language processing, and the construction of social tools and platforms. However, Cooperative AI is not the union of these existing areas, but rather an independent bet about the productivity of specific kinds of conversations that involve these and other areas. We see opportunity to more explicitly focus on the problem of cooperation, to construct unified theory and vocabulary, and to build bridges with adjacent communities working on cooperation, including in the natural, social, and behavioural sciences.

We present DeepMind Lab2D, a scalable environment simulator for artificial intelligence research that facilitates researcher-led experimentation with environment design. DeepMind Lab2D was built with the specific needs of multi-agent deep reinforcement learning researchers in mind, but it may also be useful beyond that particular subfield., Comment: 7 pages, 2 figures

When autonomous agents interact in the same environment, they must often cooperate to achieve their goals. One way for agents to cooperate effectively is to form a team, make a binding agreement on a joint plan, and execute it. However, when agents are self-interested, the gains from team formation must be allocated appropriately to incentivize agreement. Various approaches for multi-agent negotiation have been proposed, but typically only work for particular negotiation protocols. More general methods usually require human input or domain-specific data, and so do not scale. To address this, we propose a framework for training agents to negotiate and form teams using deep reinforcement learning. Importantly, our method makes no assumptions about the specific negotiation protocol, and is instead completely experience driven. We evaluate our approach on both non-spatial and spatially extended team-formation negotiation environments, demonstrating that our agents beat hand-crafted bots and reach negotiation outcomes consistent with fair solutions predicted by cooperative game theory. Additionally, we investigate how the physical location of agents influences negotiation outcomes.

Game theoretic views of convention generally rest on notions of common knowledge and hyper-rational models of individual behavior. However, decades of work in behavioral economics have questioned the validity of both foundations. Meanwhile, computational neuroscience has contributed a modernized 'dual process' account of decision-making where model-free (MF) reinforcement learning trades off with model-based (MB) reinforcement learning. The former captures habitual and procedural learning while the latter captures choices taken via explicit planning and deduction. Some conventions (e.g. international treaties) are likely supported by cognition that resonates with the game theoretic and MB accounts. However, convention formation may also occur via MF mechanisms like habit learning; though this possibility has been understudied. Here, we demonstrate that complex, large-scale conventions can emerge from MF learning mechanisms. This suggests that some conventions may be supported by habit-like cognition rather than explicit reasoning. We apply MF multi-agent reinforcement learning to a temporo-spatially extended game with incomplete information. In this game, large parts of the state space are reachable only by collective action. However, heterogeneity of tastes makes such coordinated action difficult: multiple equilibria are desirable for all players, but subgroups prefer a particular equilibrium over all others. This creates a coordination problem that can be solved by establishing a convention. We investigate start-up and free rider subproblems as well as the effects of group size, intensity of intrinsic preference, and salience on the emergence dynamics of coordination conventions. Results of our simulations show agents establish and switch between conventions, even working against their own preferred outcome when doing so is necessary for effective coordination.

Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. What's more, competition is a vital mechanism in many real-world multi-agent systems capable of generating intelligent innovations: Darwinian evolution, the market economy and the AlphaZero algorithm, to name a few. In two-player zero-sum games, the challenge is usually viewed as finding Nash equilibrium strategies, safeguarding against exploitation regardless of the opponent. While this captures the intricacies of chess or Go, it avoids the notion of cooperation with co-players, a hallmark of the major transitions leading from unicellular organisms to human civilization. Beyond two players, alliance formation often confers an advantage; however this requires trust, namely the promise of mutual cooperation in the face of incentives to defect. Successful play therefore requires adaptation to co-players rather than the pursuit of non-exploitability. Here we argue that a systematic study of many-player zero-sum games is a crucial element of artificial intelligence research. Using symmetric zero-sum matrix games, we demonstrate formally that alliance formation may be seen as a social dilemma, and empirically that na\"ive multi-agent reinforcement learning therefore fails to form alliances. We introduce a toy model of economic competition, and show how reinforcement learning may be augmented with a peer-to-peer contract mechanism to discover and enforce alliances. Finally, we generalize our agent model to incorporate temporally-extended contracts, presenting opportunities for further work., Comment: Accepted for publication at AAMAS 2020

Recent research on reinforcement learning in pure-conflict and pure-common interest games has emphasized the importance of population heterogeneity. In contrast, studies of reinforcement learning in mixed-motive games have primarily leveraged homogeneous approaches. Given the defining characteristic of mixed-motive games--the imperfect correlation of incentives between group members--we study the effect of population heterogeneity on mixed-motive reinforcement learning. We draw on interdependence theory from social psychology and imbue reinforcement learning agents with Social Value Orientation (SVO), a flexible formalization of preferences over group outcome distributions. We subsequently explore the effects of diversity in SVO on populations of reinforcement learning agents in two mixed-motive Markov games. We demonstrate that heterogeneity in SVO generates meaningful and complex behavioral variation among agents similar to that suggested by interdependence theory. Empirical results in these mixed-motive dilemmas suggest agents trained in heterogeneous populations develop particularly generalized, high-performing policies relative to those trained in homogeneous populations., Comment: Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2020)

How can societies learn to enforce and comply with social norms? Here we investigate the learning dynamics and emergence of compliance and enforcement of social norms in a foraging game, implemented in a multi-agent reinforcement learning setting. In this spatiotemporally extended game, individuals are incentivized to implement complex berry-foraging policies and punish transgressions against social taboos covering specific berry types. We show that agents benefit when eating poisonous berries is taboo, meaning the behavior is punished by other agents, as this helps overcome a credit-assignment problem in discovering delayed health effects. Critically, however, we also show that introducing an additional taboo, which results in punishment for eating a harmless berry, improves the rate and stability with which agents learn to punish taboo violations and comply with taboos. Counterintuitively, our results show that an arbitrary taboo (a "silly rule") can enhance social learning dynamics and achieve better outcomes in the middle stages of learning. We discuss the results in the context of studying normativity as a group-level emergent phenomenon.

With the success of modern machine learning, it is becoming increasingly important to understand and control how learning algorithms interact. Unfortunately, negative results from game theory show there is little hope of understanding or controlling general n-player games. We therefore introduce smooth markets (SM-games), a class of n-player games with pairwise zero sum interactions. SM-games codify a common design pattern in machine learning that includes (some) GANs, adversarial training, and other recent algorithms. We show that SM-games are amenable to analysis and optimization using first-order methods., Comment: 18 pages, 3 figures

Memory is an important aspect of intelligence and plays a role in many deep reinforcement learning models. However, little progress has been made in understanding when specific memory systems help more than others and how well they generalize. The field also has yet to see a prevalent consistent and rigorous approach for evaluating agent performance on holdout data. In this paper, we aim to develop a comprehensive methodology to test different kinds of memory in an agent and assess how well the agent can apply what it learns in training to a holdout set that differs from the training set along dimensions that we suggest are relevant for evaluating memory-specific generalization. To that end, we first construct a diverse set of memory tasks that allow us to evaluate test-time generalization across multiple dimensions. Second, we develop and perform multiple ablations on an agent architecture that combines multiple memory systems, observe its baseline models, and investigate its performance against the task suite., Comment: NeurIPS 2019. Equal contribution of first 4 authors

This paper investigates generalisation in multi-agent games, where the generality of the agent can be evaluated by playing against opponents it hasn't seen during training. We propose two new games with concealed information and complex, non-transitive reward structure (think rock/paper/scissors). It turns out that most current deep reinforcement learning methods fail to efficiently explore the strategy space, thus learning policies that generalise poorly to unseen opponents. We then propose a novel hierarchical agent architecture, where the hierarchy is grounded in the game-theoretic structure of the game -- the top level chooses strategic responses to opponents, while the low level implements them into policy over primitive actions. This grounding facilitates credit assignment across the levels of hierarchy. Our experiments show that the proposed hierarchical agent is capable of generalisation to unseen opponents, while conventional baselines fail to generalise whatsoever., Comment: First two authors contributed equally

The measurement of time is central to intelligent behavior. We know that both animals and artificial agents can successfully use temporal dependencies to select actions. In artificial agents, little work has directly addressed (1) which architectural components are necessary for successful development of this ability, (2) how this timing ability comes to be represented in the units and actions of the agent, and (3) whether the resulting behavior of the system converges on solutions similar to those of biology. Here we studied interval timing abilities in deep reinforcement learning agents trained end-to-end on an interval reproduction paradigm inspired by experimental literature on mechanisms of timing. We characterize the strategies developed by recurrent and feedforward agents, which both succeed at temporal reproduction using distinct mechanisms, some of which bear specific and intriguing similarities to biological systems. These findings advance our understanding of how agents come to represent time, and they highlight the value of experimentally inspired approaches to characterizing agent abilities., Comment: 11 pages, 7 figures

Reciprocity is an important feature of human social interaction and underpins our cooperative nature. What is more, simple forms of reciprocity have proved remarkably resilient in matrix game social dilemmas. Most famously, the tit-for-tat strategy performs very well in tournaments of Prisoner's Dilemma. Unfortunately this strategy is not readily applicable to the real world, in which options to cooperate or defect are temporally and spatially extended. Here, we present a general online reinforcement learning algorithm that displays reciprocal behavior towards its co-players. We show that it can induce pro-social outcomes for the wider group when learning alongside selfish agents, both in a $2$-player Markov game, and in $5$-player intertemporal social dilemmas. We analyse the resulting policies to show that the reciprocating agents are strongly influenced by their co-players' behavior.

Evolution has produced a multi-scale mosaic of interacting adaptive units. Innovations arise when perturbations push parts of the system away from stable equilibria into new regimes where previously well-adapted solutions no longer work. Here we explore the hypothesis that multi-agent systems sometimes display intrinsic dynamics arising from competition and cooperation that provide a naturally emergent curriculum, which we term an autocurriculum. The solution of one social task often begets new social tasks, continually generating novel challenges, and thereby promoting innovation. Under certain conditions these challenges may become increasingly complex over time, demanding that agents accumulate ever more innovations., Comment: 16 pages, 2 figures

Here we explore a new algorithmic framework for multi-agent reinforcement learning, called Malthusian reinforcement learning, which extends self-play to include fitness-linked population size dynamics that drive ongoing innovation. In Malthusian RL, increases in a subpopulation's average return drive subsequent increases in its size, just as Thomas Malthus argued in 1798 was the relationship between preindustrial income levels and population growth. Malthusian reinforcement learning harnesses the competitive pressures arising from growing and shrinking population size to drive agents to explore regions of state and policy spaces that they could not otherwise reach. Furthermore, in environments where there are potential gains from specialization and division of labor, we show that Malthusian reinforcement learning is better positioned to take advantage of such synergies than algorithms based on self-play., Comment: 9 pages, 2 tables, 4 figures

Multi-agent cooperation is an important feature of the natural world. Many tasks involve individual incentives that are misaligned with the common good, yet a wide range of organisms from bacteria to insects and humans are able to overcome their differences and collaborate. Therefore, the emergence of cooperative behavior amongst self-interested individuals is an important question for the fields of multi-agent reinforcement learning (MARL) and evolutionary theory. Here, we study a particular class of multi-agent problems called intertemporal social dilemmas (ISDs), where the conflict between the individual and the group is particularly sharp. By combining MARL with appropriately structured natural selection, we demonstrate that individual inductive biases for cooperation can be learned in a model-free way. To achieve this, we introduce an innovative modular architecture for deep reinforcement learning agents which supports multi-level selection. We present results in two challenging environments, and interpret these in the context of cultural and ecological evolution., Comment: 10 pages, 6 figures. In Proc. of the 18th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2019)

We propose a unified mechanism for achieving coordination and communication in Multi-Agent Reinforcement Learning (MARL), through rewarding agents for having causal influence over other agents' actions. Causal influence is assessed using counterfactual reasoning. At each timestep, an agent simulates alternate actions that it could have taken, and computes their effect on the behavior of other agents. Actions that lead to bigger changes in other agents' behavior are considered influential and are rewarded. We show that this is equivalent to rewarding agents for having high mutual information between their actions. Empirical results demonstrate that influence leads to enhanced coordination and communication in challenging social dilemma environments, dramatically increasing the learning curves of the deep RL agents, and leading to more meaningful learned communication protocols. The influence rewards for all agents can be computed in a decentralized way by enabling agents to learn a model of other agents using deep neural networks. In contrast, key previous works on emergent communication in the MARL setting were unable to learn diverse policies in a decentralized manner and had to resort to centralized training. Consequently, the influence reward opens up a window of new opportunities for research in this area.

Recent progress in artificial intelligence through reinforcement learning (RL) has shown great success on increasingly complex single-agent environments and two-player turn-based games. However, the real-world contains multiple agents, each learning and acting independently to cooperate and compete with other agents, and environments reflecting this degree of complexity remain an open challenge. In this work, we demonstrate for the first time that an agent can achieve human-level in a popular 3D multiplayer first-person video game, Quake III Arena Capture the Flag, using only pixels and game points as input. These results were achieved by a novel two-tier optimisation process in which a population of independent RL agents are trained concurrently from thousands of parallel matches with agents playing in teams together and against each other on randomly generated environments. Each agent in the population learns its own internal reward signal to complement the sparse delayed reward from winning, and selects actions using a novel temporally hierarchical representation that enables the agent to reason at multiple timescales. During game-play, these agents display human-like behaviours such as navigating, following, and defending based on a rich learned representation that is shown to encode high-level game knowledge. In an extensive tournament-style evaluation the trained agents exceeded the win-rate of strong human players both as teammates and opponents, and proved far stronger than existing state-of-the-art agents. These results demonstrate a significant jump in the capabilities of artificial agents, bringing us closer to the goal of human-level intelligence.

Multi-agent reinforcement learning offers a way to study how communication could emerge in communities of agents needing to solve specific problems. In this paper, we study the emergence of communication in the negotiation environment, a semi-cooperative model of agent interaction. We introduce two communication protocols -- one grounded in the semantics of the game, and one which is \textit{a priori} ungrounded and is a form of cheap talk. We show that self-interested agents can use the pre-grounded communication channel to negotiate fairly, but are unable to effectively use the ungrounded channel. However, prosocial agents do learn to use cheap talk to find an optimal negotiating strategy, suggesting that cooperation is necessary for language to emerge. We also study communication behaviour in a setting where one agent interacts with agents in a community with different levels of prosociality and show how agent identifiability can aid negotiation., Comment: Published as a conference paper at ICLR 2018

Animals execute goal-directed behaviours despite the limited range and scope of their sensors. To cope, they explore environments and store memories maintaining estimates of important information that is not presently available. Recently, progress has been made with artificial intelligence (AI) agents that learn to perform tasks from sensory input, even at a human level, by merging reinforcement learning (RL) algorithms with deep neural networks, and the excitement surrounding these results has led to the pursuit of related ideas as explanations of non-human animal learning. However, we demonstrate that contemporary RL algorithms struggle to solve simple tasks when enough information is concealed from the sensors of the agent, a property called "partial observability". An obvious requirement for handling partially observed tasks is access to extensive memory, but we show memory is not enough; it is critical that the right information be stored in the right format. We develop a model, the Memory, RL, and Inference Network (MERLIN), in which memory formation is guided by a process of predictive modeling. MERLIN facilitates the solution of tasks in 3D virtual reality environments for which partial observability is severe and memories must be maintained over long durations. Our model demonstrates a single learning agent architecture that can solve canonical behavioural tasks in psychology and neurobiology without strong simplifying assumptions about the dimensionality of sensory input or the duration of experiences.

Groups of humans are often able to find ways to cooperate with one another in complex, temporally extended social dilemmas. Models based on behavioral economics are only able to explain this phenomenon for unrealistic stateless matrix games. Recently, multi-agent reinforcement learning has been applied to generalize social dilemma problems to temporally and spatially extended Markov games. However, this has not yet generated an agent that learns to cooperate in social dilemmas as humans do. A key insight is that many, but not all, human individuals have inequity averse social preferences. This promotes a particular resolution of the matrix game social dilemma wherein inequity-averse individuals are personally pro-social and punish defectors. Here we extend this idea to Markov games and show that it promotes cooperation in several types of sequential social dilemma, via a profitable interaction with policy learnability. In particular, we find that inequity aversion improves temporal credit assignment for the important class of intertemporal social dilemmas. These results help explain how large-scale cooperation may emerge and persist., Comment: 15 pages, 8 figures

This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash equilibrium of the true underlying game. We investigate and show how many data samples are required to obtain a close enough approximation of the underlying game. Additionally, we extend the meta-game analysis methodology to asymmetric games. The state-of-the-art has only considered empirical games in which agents have access to the same strategy sets and the payoff structure is symmetric, implying that agents are interchangeable. Finally, we carry out an empirical illustration of the generalised method in several domains, illustrating the theory and evolutionary dynamics of several versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel Blotto game played by human players on Facebook (symmetric), and an example of a meta-game in Leduc Poker (asymmetric), generated by the PSRO multi-agent learning algorithm., Comment: will appear at AAMAS'18

We present a method for using previously-trained 'teacher' agents to kickstart the training of a new 'student' agent. To this end, we leverage ideas from policy distillation and population based training. Our method places no constraints on the architecture of the teacher or student agents, and it regulates itself to allow the students to surpass their teachers in performance. We show that, on a challenging and computationally-intensive multi-task benchmark (DMLab-30), kickstarted training improves the data efficiency of new agents, making it significantly easier to iterate on their design. We also show that the same kickstarting pipeline can allow a single student agent to leverage multiple 'expert' teachers which specialize on individual tasks. In this setting kickstarting yields surprisingly large gains, with the kickstarted agent matching the performance of an agent trained from scratch in almost 10x fewer steps, and surpassing its final performance by 42 percent. Kickstarting is conceptually simple and can easily be incorporated into reinforcement learning experiments.

Psychlab is a simulated psychology laboratory inside the first-person 3D game world of DeepMind Lab (Beattie et al. 2016). Psychlab enables implementations of classical laboratory psychological experiments so that they work with both human and artificial agents. Psychlab has a simple and flexible API that enables users to easily create their own tasks. As examples, we are releasing Psychlab implementations of several classical experimental paradigms including visual search, change detection, random dot motion discrimination, and multiple object tracking. We also contribute a study of the visual psychophysics of a specific state-of-the-art deep reinforcement learning agent: UNREAL (Jaderberg et al. 2016). This study leads to the surprising conclusion that UNREAL learns more quickly about larger target stimuli than it does about smaller stimuli. In turn, this insight motivates a specific improvement in the form of a simple model of foveal vision that turns out to significantly boost UNREAL's performance, both on Psychlab tasks, and on standard DeepMind Lab tasks. By open-sourcing Psychlab we hope to facilitate a range of future such studies that simultaneously advance deep reinforcement learning and improve its links with cognitive science., Comment: 28 pages, 11 figures

Humanity faces numerous problems of common-pool resource appropriation. This class of multi-agent social dilemma includes the problems of ensuring sustainable use of fresh water, common fisheries, grazing pastures, and irrigation systems. Abstract models of common-pool resource appropriation based on non-cooperative game theory predict that self-interested agents will generally fail to find socially positive equilibria---a phenomenon called the tragedy of the commons. However, in reality, human societies are sometimes able to discover and implement stable cooperative solutions. Decades of behavioral game theory research have sought to uncover aspects of human behavior that make this possible. Most of that work was based on laboratory experiments where participants only make a single choice: how much to appropriate. Recognizing the importance of spatial and temporal resource dynamics, a recent trend has been toward experiments in more complex real-time video game-like environments. However, standard methods of non-cooperative game theory can no longer be used to generate predictions for this case. Here we show that deep reinforcement learning can be used instead. To that end, we study the emergent behavior of groups of independently learning agents in a partially observed Markov game modeling common-pool resource appropriation. Our experiments highlight the importance of trial-and-error learning in common-pool resource appropriation and shed light on the relationship between exclusion, sustainability, and inequality., Comment: 15 pages, 11 figures

We study the problem of cooperative multi-agent reinforcement learning with a single joint reward signal. This class of learning problems is difficult because of the often large combined action and observation spaces. In the fully centralized and decentralized approaches, we find the problem of spurious rewards and a phenomenon we call the "lazy agent" problem, which arises due to partial observability. We address these problems by training individual agents with a novel value decomposition network architecture, which learns to decompose the team value function into agent-wise value functions. We perform an experimental evaluation across a range of partially-observable multi-agent domains and show that learning such value-decompositions leads to superior results, in particular when combined with weight sharing, role information and information channels.