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Recent work has considered whether large language models (LLMs) can function as planners: given a task, generate a plan. We investigate whether LLMs can serve as generalized planners: given a domain and training tasks, generate a program that efficiently produces plans for other tasks in the domain. In particular, we consider PDDL domains and use GPT-4 to synthesize Python programs. We also consider (1) Chain-of-Thought (CoT) summarization, where the LLM is prompted to summarize the domain and propose a strategy in words before synthesizing the program; and (2) automated debugging, where the program is validated with respect to the training tasks, and in case of errors, the LLM is re-prompted with four types of feedback. We evaluate this approach in seven PDDL domains and compare it to four ablations and four baselines. Overall, we find that GPT-4 is a surprisingly powerful generalized planner. We also conclude that automated debugging is very important, that CoT summarization has non-uniform impact, that GPT-4 is far superior to GPT-3.5, and that just two training tasks are often sufficient for strong generalization., Comment: AAAI 2024

We generalize the Approximate Quantum Compiling algorithm into a new method for CNOT-depth reduction, which is apt to process wide target quantum circuits. Combining this method with state-of-the-art techniques for error mitigation and circuit compiling, we present a 10-qubit experimental demonstration of Iterative Amplitude Estimation on a quantum computer. The target application is the derivation of the Expected Value of contract portfolios in the energy industry. In parallel, we also introduce a new variant of the Quantum Amplitude Estimation algorithm which we call Dynamic Amplitude Estimation, as it is based on the dynamic circuit capability of quantum devices. The algorithm achieves a reduction in the circuit width in the order of the binary precision compared to the typical implementation of Quantum Amplitude Estimation, while simultaneously decreasing the number of quantum-classical iterations (again in the order of the binary precision) compared to the Iterative Amplitude Estimation. The calculation of the Expected Value, VaR and CVaR of contract portfolios on quantum hardware provides a proof of principle of the new algorithm., Comment: 25 pages, 11 figures, 5 tables

We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of providers) is fixed, and dictated by the size of the market. The game thus captures the tension between resource pooling (to benefit from the resulting statistical economies of scale) and competition between coalitions over market share. In a departure from the prior literature on resource pooling for congestible services, we show that the grand coalition is in general not stable, once we allow for competition over market share. In fact, under classical notions of stability (defined via blocking by any coalition), we show that no partition is stable. This motivates us to introduce more restricted (and relevant) notions of blocking; interestingly, we find that the stable configurations under these novel notions of stability are duopolies, where the dominant coalition exploits its economies of scale to corner a disproportionate market share. Furthermore, we completely characterise the stable duopolies in heavy and light traffic regimes., Comment: arXiv admin note: text overlap with arXiv:2109.12840

Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions of scenarios, largely benefiting from computational speedups. We develop a novel hybrid quantum-classical algorithm based on polynomial approximation of nonlinear functions, computed through Quantum Hadamard Products, and we rigorously assess the conditions for its end-to-end speedup for different implementation variants against classical algorithms. In our setting, a quadratic quantum speedup, up to polylogarithmic factors, can be proven only when forms are bilinear and approximating polynomials have second degree, if efficient loading unitaries are available for the input data sets. We also enhance the bidirectional encoding, that allows tuning the balance between circuit depth and width, proposing an improved version that can be exploited for the calculation of inner products. Lastly, we exploit the dynamic circuit capabilities, recently introduced on IBM Quantum devices, to reduce the average depth of the Quantum Hadamard Product circuit. A proof of principle is implemented and validated on IBM Quantum systems.

Celebrities can significantly influence the public towards any desired outcome. In a bid to tackle an infectious disease, a leader (government) exploits such influence towards motivating a fraction of public to get vaccinated, sufficient enough to ensure eradication. The leader also aims to minimize the vaccinated fraction of public (that ensures eradication) and use minimal incentives to motivate the influencers; it also controls vaccine-supply-rates. Towards this, we consider a three-layered Stackelberg game, with the leader at the top. A set of influencers at the middle layer are involved in a stochastic vaccination game driven by incentives. The public at the bottom layer is involved in an evolutionary game with respect to vaccine responses. We prove the disease can always be eradicated once the public is sufficiently sensitive towards the vaccination choices of the influencers -- with a minimal fraction of public vaccinated. This minimal fraction depends only on the disease characteristics and not on other aspects. Interestingly, there are many configurations to achieve eradication, each configuration is specified by a dynamic vaccine-supply-rate and a number -- this number represents the count of the influencers that needs to be vaccinated to achieve the desired influence. Incentive schemes are optimal when this number equals all or just one; the former curbs free-riding among influencers while the latter minimizes the dependency on influencers., Comment: 50 pages, 6 figures

Crowd-sourcing models, which leverage the collective opinions/signals of users on online social networks (OSNs), are well-accepted for fake post detection; however, motivating the users to provide the crowd signals is challenging, even more so in the presence of adversarial users. We design a participation (mean-field) game where users of the OSN are lured by a reward-based scheme to provide the binary (real/fake) signals such that the OSN achieves $(\theta, \delta)$-level of actuality identification (AI) - not more than $\delta$ fraction of non-adversarial users incorrectly judge the real post, and at least $\theta$ fraction of non-adversarial users identify the fake post as fake. An appropriate warning mechanism is proposed to influence the decision-making of the users such that the resultant game has at least one Nash Equilibrium (NE) achieving AI. We also identify the conditions under which all NEs achieve AI. Further, we numerically illustrate that one can always design an AI game if the normalized difference in the innate identification capacities of the users is at least $1\%$, when desired $\theta = 75\%$., Comment: 11 pages, 1 figure, 1 algorithm

This paper considers the problem of finding a solution to the finite horizon constrained Markov decision processes (CMDP) where the objective as well as constraints are sum of additive and multiplicative utilities. Towards solving this, we construct another CMDP, with only additive utilities under a restricted set of policies, whose optimal value is equal to that of the original CMDP. Furthermore, we provide a finite dimensional bilinear program (BLP) whose value equals the CMDP value and whose solution provides the optimal policy. We also suggest an algorithm to solve this BLP.

The COVID-19 pandemic has witnessed the role of online social networks (OSNs) in the spread of infectious diseases. The rise in severity of the epidemic augments the need for proper guidelines, but also promotes the propagation of fake news-items. The popularity of a news-item can reshape the public health behaviors and affect the epidemic processes. There is a clear inter-dependency between the epidemic process and the spreading of news-items. This work creates an integrative framework to understand the interplay. We first develop a population-dependent `saturated branching process' to continually track the propagation of trending news-items on OSNs. A two-time scale dynamical system is obtained by integrating the news-propagation model with SIRS epidemic model, to analyze the holistic system. It is observed that a pattern of periodic infections emerges under a linear behavioral influence, which explains the waves of infection and reinfection that we have experienced in the pandemic. We use numerical experiments to corroborate the results and use Twitter and COVID-19 data-sets to recreate the historical infection curve using the integrative model.

The recent efforts in automation of machine learning or data science has achieved success in various tasks such as hyper-parameter optimization or model selection. However, key areas such as utilizing domain knowledge and data semantics are areas where we have seen little automation. Data Scientists have long leveraged common sense reasoning and domain knowledge to understand and enrich data for building predictive models. In this paper we discuss important shortcomings of current data science and machine learning solutions. We then envision how leveraging "semantic" understanding and reasoning on data in combination with novel tools for data science automation can help with consistent and explainable data augmentation and transformation. Additionally, we discuss how semantics can assist data scientists in a new manner by helping with challenges related to trust, bias, and explainability in machine learning. Semantic annotation can also help better explore and organize large data sources., Comment: arXiv admin note: substantial text overlap with arXiv:2205.08018