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Recommender systems are an important part of the modern human experience whose influence ranges from the food we eat to the news we read. Yet, there is still debate as to what extent recommendation platforms are aligned with the user goals. A core issue fueling this debate is the challenge of inferring a user utility based on engagement signals such as likes, shares, watch time etc., which are the primary metric used by platforms to optimize content. This is because users utility-driven decision-processes (which we refer to as System-2), e.g., reading news that are relevant for them, are often confounded by their impulsive decision-processes (which we refer to as System-1), e.g., spend time on click-bait news. As a result, it is difficult to infer whether an observed engagement is utility-driven or impulse-driven. In this paper we explore a new approach to recommender systems where we infer user utility based on their return probability to the platform rather than engagement signals. Our intuition is that users tend to return to a platform in the long run if it creates utility for them, while pure engagement-driven interactions that do not add utility, may affect user return in the short term but will not have a lasting effect. We propose a generative model in which past content interactions impact the arrival rates of users based on a self-exciting Hawkes process. These arrival rates to the platform are a combination of both System-1 and System-2 decision processes. The System-2 arrival intensity depends on the utility and has a long lasting effect, while the System-1 intensity depends on the instantaneous gratification and tends to vanish rapidly. We show analytically that given samples it is possible to disentangle System-1 and System-2 and allow content optimization based on user utility. We conduct experiments on synthetic data to demonstrate the effectiveness of our approach., Comment: Accepted at FAccT'24

In dueling bandits, the learner receives preference feedback between arms, and the regret of an arm is defined in terms of its suboptimality to a winner arm. The more challenging and practically motivated non-stationary variant of dueling bandits, where preferences change over time, has been the focus of several recent works (Saha and Gupta, 2022; Buening and Saha, 2023; Suk and Agarwal, 2023). The goal is to design algorithms without foreknowledge of the amount of change. The bulk of known results here studies the Condorcet winner setting, where an arm preferred over any other exists at all times. Yet, such a winner may not exist and, to contrast, the Borda version of this problem (which is always well-defined) has received little attention. In this work, we establish the first optimal and adaptive Borda dynamic regret upper bound, which highlights fundamental differences in the learnability of severe non-stationarity between Condorcet vs. Borda regret objectives in dueling bandits. Surprisingly, our techniques for non-stationary Borda dueling bandits also yield improved rates within the Condorcet winner setting, and reveal new preference models where tighter notions of non-stationarity are adaptively learnable. This is accomplished through a novel generalized Borda score framework which unites the Borda and Condorcet problems, thus allowing reduction of Condorcet regret to a Borda-like task. Such a generalization was not previously known and is likely to be of independent interest.

Compliant grippers enable robots to work with humans in unstructured environments. In general, these grippers can improve with tactile sensing to estimate the state of objects around them to precisely manipulate objects. However, co-designing compliant structures with high-resolution tactile sensing is a challenging task. We propose a simulation framework for the end-to-end forward design of GelSight Fin Ray sensors. Our simulation framework consists of mechanical simulation using the finite element method (FEM) and optical simulation including physically based rendering (PBR). To simulate the fluorescent paint used in these GelSight Fin Rays, we propose an efficient method that can be directly integrated in PBR. Using the simulation framework, we investigate design choices available in the compliant grippers, namely gel pad shapes, illumination conditions, Fin Ray gripper sizes, and Fin Ray stiffness. This infrastructure enables faster design and prototype time frames of new Fin Ray sensors that have various sensing areas, ranging from 48 mm $\times$ \18 mm to 70 mm $\times$ 35 mm. Given the parameters we choose, we can thus optimize different Fin Ray designs and show their utility in grasping day-to-day objects., Comment: Yuxiang Ma, Arpit Agarwal, and Sandra Q. Liu contributed equally to this work. Project video: https://youtu.be/CnTUTA5cfMw . 7 pages, 11 figures, 2024 IEEE International Conference on Soft Robotics (RoboSoft)

We present a parallel algorithm for the $(1-\epsilon)$-approximate maximum flow problem in capacitated, undirected graphs with $n$ vertices and $m$ edges, achieving $O(\epsilon^{-3}\text{polylog} n)$ depth and $O(m \epsilon^{-3} \text{polylog} n)$ work in the PRAM model. Although near-linear time sequential algorithms for this problem have been known for almost a decade, no parallel algorithms that simultaneously achieved polylogarithmic depth and near-linear work were known. At the heart of our result is a polylogarithmic depth, near-linear work recursive algorithm for computing congestion approximators. Our algorithm involves a recursive step to obtain a low-quality congestion approximator followed by a "boosting" step to improve its quality which prevents a multiplicative blow-up in error. Similar to Peng [SODA'16], our boosting step builds upon the hierarchical decomposition scheme of R\"acke, Shah, and T\"aubig [SODA'14]. A direct implementation of this approach, however, leads only to an algorithm with $n^{o(1)}$ depth and $m^{1+o(1)}$ work. To get around this, we introduce a new hierarchical decomposition scheme, in which we only need to solve maximum flows on subgraphs obtained by contracting vertices, as opposed to vertex-induced subgraphs used in R\"acke, Shah, and T\"aubig [SODA'14]. In particular, we are able to directly extract congestion approximators for the subgraphs from a congestion approximator for the entire graph, thereby avoiding additional recursion on those subgraphs. Along the way, we also develop a parallel flow-decomposition algorithm that is crucial to achieving polylogarithmic depth and may be of independent interest.

In digital health and EdTech, recommendation systems face a significant challenge: users often choose impulsively, in ways that conflict with the platform's long-term payoffs. This misalignment makes it difficult to effectively learn to rank items, as it may hinder exploration of items with greater long-term payoffs. Our paper tackles this issue by utilizing users' limited attention spans. We propose a model where a platform presents items with unknown payoffs to the platform in a ranked list to $T$ users over time. Each user selects an item by first considering a prefix window of these ranked items and then picking the highest preferred item in that window (and the platform observes its payoff for this item). We study the design of online bandit algorithms that obtain vanishing regret against hindsight optimal benchmarks. We first consider adversarial window sizes and stochastic iid payoffs. We design an active-elimination-based algorithm that achieves an optimal instance-dependent regret bound of $O(\log(T))$, by showing matching regret upper and lower bounds. The key idea is using the combinatorial structure of the problem to either obtain a large payoff from each item or to explore by getting a sample from that item. This method systematically narrows down the item choices to enhance learning efficiency and payoff. Second, we consider adversarial payoffs and stochastic iid window sizes. We start from the full-information problem of finding the permutation that maximizes the expected payoff. By a novel combinatorial argument, we characterize the polytope of admissible item selection probabilities by a permutation and show it has a polynomial-size representation. Using this representation, we show how standard algorithms for adversarial online linear optimization in the space of admissible probabilities can be used to obtain a polynomial-time algorithm with $O(\sqrt{T})$ regret.

Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in this area. However, a significant limitation of this approach is that it requires full knowledge of the underlying probability distributions. Can we still get good (approximation) algorithms if these distributions are unknown, and the algorithm needs to learn them through repeated interactions? In this paper, we resolve this question for a large class of "monotone" stochastic problems, by providing a generic online learning algorithm with $\sqrt{T \log T}$ regret relative to the best approximation algorithm (under known distributions). Importantly, our online algorithm works in a semi-bandit setting, where in each period, the algorithm only observes samples from the r.v.s that were actually probed. Our framework applies to several fundamental problems in stochastic optimization such as prophet inequality, Pandora's box, stochastic knapsack, stochastic matchings and stochastic submodular optimization.

In dynamic submodular maximization, the goal is to maintain a high-value solution over a sequence of element insertions and deletions with a fast update time. Motivated by large-scale applications and the fact that dynamic data often exhibits patterns, we ask the following question: can predictions be used to accelerate the update time of dynamic submodular maximization algorithms? We consider the model for dynamic algorithms with predictions where predictions regarding the insertion and deletion times of elements can be used for preprocessing. Our main result is an algorithm with an $O(poly(\log \eta, \log w, \log k))$ amortized update time over the sequence of updates that achieves a $1/2 - \epsilon$ approximation in expectation for dynamic monotone submodular maximization under a cardinality constraint $k$, where the prediction error $\eta$ is the number of elements that are not inserted and deleted within $w$ time steps of their predicted insertion and deletion times. This amortized update time is independent of the length of the stream and instead depends on the prediction error.

In manufacturing processes, surface inspection is a key requirement for quality assessment and damage localization. Due to this, automated surface anomaly detection has become a promising area of research in various industrial inspection systems. A particular challenge in industries with large-scale components, like aircraft and heavy machinery, is inspecting large parts with very small defect dimensions. Moreover, these parts can be of curved shapes. To address this challenge, we present a 2-stage multi-modal inspection pipeline with visual and tactile sensing. Our approach combines the best of both visual and tactile sensing by identifying and localizing defects using a global view (vision) and using the localized area for tactile scanning for identifying remaining defects. To benchmark our approach, we propose a novel real-world dataset with multiple metallic defect types per image, collected in the production environments on real aerospace manufacturing parts, as well as online robot experiments in two environments. Our approach is able to identify 85% defects using Stage I and identify 100% defects after Stage II. The dataset is publicly available at https://zenodo.org/record/8327713, Comment: This is a pre-print for International Conference on Intelligent Robots and Systems 2023 publication

The $K$-armed dueling bandits problem, where the feedback is in the form of noisy pairwise preferences, has been widely studied due its applications in information retrieval, recommendation systems, etc. Motivated by concerns that user preferences/tastes can evolve over time, we consider the problem of dueling bandits with distribution shifts. Specifically, we study the recent notion of significant shifts (Suk and Kpotufe, 2022), and ask whether one can design an adaptive algorithm for the dueling problem with $O(\sqrt{K\tilde{L}T})$ dynamic regret, where $\tilde{L}$ is the (unknown) number of significant shifts in preferences. We show that the answer to this question depends on the properties of underlying preference distributions. Firstly, we give an impossibility result that rules out any algorithm with $O(\sqrt{K\tilde{L}T})$ dynamic regret under the well-studied Condorcet and SST classes of preference distributions. Secondly, we show that $\text{SST} \cap \text{STI}$ is the largest amongst popular classes of preference distributions where it is possible to design such an algorithm. Overall, our results provides an almost complete resolution of the above question for the hierarchy of distribution classes.

We consider a bandit recommendations problem in which an agent's preferences (representing selection probabilities over recommended items) evolve as a function of past selections, according to an unknown $\textit{preference model}$. In each round, we show a menu of $k$ items (out of $n$ total) to the agent, who then chooses a single item, and we aim to minimize regret with respect to some $\textit{target set}$ (a subset of the item simplex) for adversarial losses over the agent's choices. Extending the setting from Agarwal and Brown (2022), where uniform-memory agents were considered, here we allow for non-uniform memory in which a discount factor is applied to the agent's memory vector at each subsequent round. In the "long-term memory" regime (when the effective memory horizon scales with $T$ sublinearly), we show that efficient sublinear regret is obtainable with respect to the set of $\textit{everywhere instantaneously realizable distributions}$ (the "EIRD set", as formulated in prior work) for any $\textit{smooth}$ preference model. Further, for preferences which are bounded above and below by linear functions of memory weight (we call these "scale-bounded" preferences) we give an algorithm which obtains efficient sublinear regret with respect to nearly the $\textit{entire}$ item simplex. We show an NP-hardness result for expanding to targets beyond EIRD in general. In the "short-term memory" regime (when the memory horizon is constant), we show that scale-bounded preferences again enable efficient sublinear regret for nearly the entire simplex even without smoothness if losses do not change too frequently, yet we show an information-theoretic barrier for competing against the EIRD set under arbitrary smooth preference models even when losses are constant., Comment: Updates for camera-ready version (ALT 2024)

We study the $K$-armed dueling bandit problem, a variation of the traditional multi-armed bandit problem in which feedback is obtained in the form of pairwise comparisons. Previous learning algorithms have focused on the $\textit{fully adaptive}$ setting, where the algorithm can make updates after every comparison. The "batched" dueling bandit problem is motivated by large-scale applications like web search ranking and recommendation systems, where performing sequential updates may be infeasible. In this work, we ask: $\textit{is there a solution using only a few adaptive rounds that matches the asymptotic regret bounds of the best sequential algorithms for $K$-armed dueling bandits?}$ We answer this in the affirmative $\textit{under the Condorcet condition}$, a standard setting of the $K$-armed dueling bandit problem. We obtain asymptotic regret of $O(K^2\log^2(K)) + O(K\log(T))$ in $O(\log(T))$ rounds, where $T$ is the time horizon. Our regret bounds nearly match the best regret bounds known in the fully sequential setting under the Condorcet condition. Finally, in computational experiments over a variety of real-world datasets, we observe that our algorithm using $O(\log(T))$ rounds achieves almost the same performance as fully sequential algorithms (that use $T$ rounds).

When an Agent visits a platform recommending a menu of content to select from, their choice of item depends not only on fixed preferences, but also on their prior engagements with the platform. The Recommender's primary objective is typically to encourage content consumption which optimizes some reward, such as ad revenue, but they often also aim to ensure that a wide variety of content is consumed by the Agent over time. We formalize this problem as an adversarial bandit task. At each step, the Recommender presents a menu of $k$ (out of $n$) items to the Agent, who selects one item in the menu according to their unknown preference model, which maps their history of past items to relative selection probabilities. The Recommender then observes the Agent's chosen item and receives bandit feedback of the item's reward. In addition to optimizing reward from selected items, the Recommender must also ensure that the total distribution of chosen items has sufficiently high entropy. We define a class of preference models which are locally learnable, i.e. behavior over the entire domain can be estimated by only observing behavior in a small region; this includes models representable by bounded-degree polynomials as well as functions with a sparse Fourier basis. For this class, we give an algorithm for the Recommender which obtains $\tilde{O}(T^{3/4})$ regret against all item distributions satisfying two conditions: they are sufficiently diversified, and they are instantaneously realizable at any history by some distribution over menus. We show that these conditions are closely connected: all sufficiently high-entropy distributions are instantaneously realizable at any item history. We also give a set of negative results justifying our assumptions, in the form of a runtime lower bound for non-local learning and linear regret lower bounds for alternate benchmarks., Comment: 34 pages, forthcoming in NeurIPS 2022

Robot simulation has been an essential tool for data-driven manipulation tasks. However, most existing simulation frameworks lack either efficient and accurate models of physical interactions with tactile sensors or realistic tactile simulation. This makes the sim-to-real transfer for tactile-based manipulation tasks still challenging. In this work, we integrate simulation of robot dynamics and vision-based tactile sensors by modeling the physics of contact. This contact model uses simulated contact forces at the robot's end-effector to inform the generation of realistic tactile outputs. To eliminate the sim-to-real transfer gap, we calibrate our physics simulator of robot dynamics, contact model, and tactile optical simulator with real-world data, and then we demonstrate the effectiveness of our system on a zero-shot sim-to-real grasp stability prediction task where we achieve an average accuracy of 90.7% on various objects. Experiments reveal the potential of applying our simulation framework to more complicated manipulation tasks. We open-source our simulation framework at https://github.com/CMURoboTouch/Taxim/tree/taxim-robot.

Hierarchical clustering over graphs is a fundamental task in data mining and machine learning with applications in domains such as phylogenetics, social network analysis, and information retrieval. Specifically, we consider the recently popularized objective function for hierarchical clustering due to Dasgupta. Previous algorithms for (approximately) minimizing this objective function require linear time/space complexity. In many applications the underlying graph can be massive in size making it computationally challenging to process the graph even using a linear time/space algorithm. As a result, there is a strong interest in designing algorithms that can perform global computation using only sublinear resources. The focus of this work is to study hierarchical clustering for massive graphs under three well-studied models of sublinear computation which focus on space, time, and communication, respectively, as the primary resources to optimize: (1) (dynamic) streaming model where edges are presented as a stream, (2) query model where the graph is queried using neighbor and degree queries, (3) MPC model where the graph edges are partitioned over several machines connected via a communication channel. We design sublinear algorithms for hierarchical clustering in all three models above. At the heart of our algorithmic results is a view of the objective in terms of cuts in the graph, which allows us to use a relaxed notion of cut sparsifiers to do hierarchical clustering while introducing only a small distortion in the objective function. Our main algorithmic contributions are then to show how cut sparsifiers of the desired form can be efficiently constructed in the query model and the MPC model. We complement our algorithmic results by establishing nearly matching lower bounds that rule out the possibility of designing better algorithms in each of these models.

The stochastic $K$-armed bandit problem has been studied extensively due to its applications in various domains ranging from online advertising to clinical trials. In practice however, the number of arms can be very large resulting in large memory requirements for simultaneously processing them. In this paper we consider a streaming setting where the arms are presented in a stream and the algorithm uses limited memory to process these arms. Here, the goal is not only to minimize regret, but also to do so in minimal memory. Previous algorithms for this problem operate in one of the two settings: they either use $\Omega(\log \log T)$ passes over the stream (Rathod, 2021; Chaudhuri and Kalyanakrishnan, 2020; Liau et al., 2018), or just a single pass (Maiti et al., 2021). In this paper we study the trade-off between memory and regret when $B$ passes over the stream are allowed, for any $B \geq 1$, and establish tight regret upper and lower bounds for any $B$-pass algorithm. Our results uncover a surprising *sharp transition phenomenon*: $O(1)$ memory is sufficient to achieve $\widetilde\Theta\Big(T^{\frac{1}{2} + \frac{1}{2^{B+2}-2}}\Big)$ regret in $B$ passes, and increasing the memory to any quantity that is $o(K)$ has almost no impact on further reducing this regret, unless we use $\Omega(K)$ memory. Our main technical contribution is our lower bound which requires the use of information-theoretic techniques as well as ideas from round elimination to show that the *residual problem* remains challenging over subsequent passes.

The $K$-armed dueling bandit problem, where the feedback is in the form of noisy pairwise comparisons, has been widely studied. Previous works have only focused on the sequential setting where the policy adapts after every comparison. However, in many applications such as search ranking and recommendation systems, it is preferable to perform comparisons in a limited number of parallel batches. We study the batched $K$-armed dueling bandit problem under two standard settings: (i) existence of a Condorcet winner, and (ii) strong stochastic transitivity and stochastic triangle inequality. For both settings, we obtain algorithms with a smooth trade-off between the number of batches and regret. Our regret bounds match the best known sequential regret bounds (up to poly-logarithmic factors), using only a logarithmic number of batches. We complement our regret analysis with a nearly-matching lower bound. Finally, we also validate our theoretical results via experiments on synthetic and real data.

Predicting the outcome of liquid droplet collisions is an extensively studied phenomenon but the current physics based models for predicting the outcomes are poor (accuracy $\approx 43\%$). The key weakness of these models is their limited complexity. They only account for 3 features while there are many more relevant features that go unaccounted for. This limitation of traditional models can be easily overcome through machine learning modeling of the problem. In an ML setting this problem directly translates to a classification problem with 4 classes. Here we compile a large labelled dataset and tune different ML classifiers over this dataset. We evaluate the accuracy and robustness of the classifiers. ML classifiers, with accuracies over 90\%, significantly outperform the physics based models. Another key question we try to answer in this paper is whether existing knowledge of the physics based models can be exploited to boost the accuracy of the ML classifiers. We find that while this knowledge improves the accuracy marginally for small datasets, it does not improve accuracy with if larger datasets are used for training the models.

Rotational displacement about the grasping point is a common grasp failure when an object is grasped at a location away from its center of gravity. Tactile sensors with soft surfaces, such as GelSight sensors, can detect the rotation patterns on the contacting surfaces when the object rotates. In this work, we propose a model-based algorithm that detects those rotational patterns and measures rotational displacement using the GelSight sensor. We also integrate the rotation detection feedback into a closed-loop regrasping framework, which detects the rotational failure of grasp in an early stage and drives the robot to a stable grasp pose. We validate our proposed rotation detection algorithm and grasp-regrasp system on self-collected dataset and online experiments to show how our approach accurately detects the rotation and increases grasp stability.

Tactile sensing has seen a rapid adoption with the advent of vision-based tactile sensors. Vision-based tactile sensors provide high resolution, compact and inexpensive data to perform precise in-hand manipulation and human-robot interaction. However, the simulation of tactile sensors is still a challenge. In this paper, we built the first fully general optical tactile simulation system for a GelSight sensor using physics-based rendering techniques. We propose physically accurate light models and show in-depth analysis of individual components of our simulation pipeline. Our system outperforms previous simulation techniques qualitatively and quantitative on image similarity metrics. Our code and experimental data is open-sourced at https://labs.ri.cmu.edu/robotouch/tactile-optical-simulation/, Comment: The paper is accepted in 2021 IEEE International Conference on Robotics and Automation. v3 updates the discussion related to figure 11 v2 incorporates the changes from the reviewers and inverse rendering optimization results

PySPH is an open-source, Python-based, framework for particle methods in general and Smoothed Particle Hydrodynamics (SPH) in particular. PySPH allows a user to define a complete SPH simulation using pure Python. High-performance code is generated from this high-level Python code and executed on either multiple cores, or on GPUs, seamlessly. It also supports distributed execution using MPI. PySPH supports a wide variety of SPH schemes and formulations. These include, incompressible and compressible fluid flow, elastic dynamics, rigid body dynamics, shallow water equations, and other problems. PySPH supports a variety of boundary conditions including mirror, periodic, solid wall, and inlet/outlet boundary conditions. The package is written to facilitate reuse and reproducibility. This paper discusses the overall design of PySPH and demonstrates many of its features. Several example results are shown to demonstrate the range of features that PySPH provides., Comment: 39 pages, 19 figures

We propose an exploration method that incorporates look-ahead search over basic learnt skills and their dynamics, and use it for reinforcement learning (RL) of manipulation policies . Our skills are multi-goal policies learned in isolation in simpler environments using existing multigoal RL formulations, analogous to options or macroactions. Coarse skill dynamics, i.e., the state transition caused by a (complete) skill execution, are learnt and are unrolled forward during lookahead search. Policy search benefits from temporal abstraction during exploration, though itself operates over low-level primitive actions, and thus the resulting policies does not suffer from suboptimality and inflexibility caused by coarse skill chaining. We show that the proposed exploration strategy results in effective learning of complex manipulation policies faster than current state-of-the-art RL methods, and converges to better policies than methods that use options or parametrized skills as building blocks of the policy itself, as opposed to guiding exploration. We show that the proposed exploration strategy results in effective learning of complex manipulation policies faster than current state-of-the-art RL methods, and converges to better policies than methods that use options or parameterized skills as building blocks of the policy itself, as opposed to guiding exploration., Comment: This is a pre-print of our paper which is accepted in AAAI 2018

We consider artificial agents that learn to jointly control their gripperand camera in order to reinforcement learn manipulation policies in the presenceof occlusions from distractor objects. Distractors often occlude the object of in-terest and cause it to disappear from the field of view. We propose hand/eye con-trollers that learn to move the camera to keep the object within the field of viewand visible, in coordination to manipulating it to achieve the desired goal, e.g.,pushing it to a target location. We incorporate structural biases of object-centricattention within our actor-critic architectures, which our experiments suggest tobe a key for good performance. Our results further highlight the importance ofcurriculum with regards to environment difficulty. The resulting active vision /manipulation policies outperform static camera setups for a variety of clutteredenvironments., Comment: The paper was present in Conference of Robot Learning 2018

In the submodular cover problem, we are given a non-negative monotone submodular function $f$ over a ground set $E$ of items, and the goal is to choose a smallest subset $S \subseteq E$ such that $f(S) = Q$ where $Q = f(E)$. In the stochastic version of the problem, we are given $m$ stochastic items which are different random variables that independently realize to some item in $E$, and the goal is to find a smallest set of stochastic items whose realization $R$ satisfies $f(R) = Q$. The problem captures as a special case the stochastic set cover problem and more generally, stochastic covering integer programs. We define an $r$-round adaptive algorithm to be an algorithm that chooses a permutation of all available items in each round $k \in [r]$, and a threshold $\tau_k$, and realizes items in the order specified by the permutation until the function value is at least $\tau_k$. The permutation for each round $k$ is chosen adaptively based on the realization in the previous rounds, but the ordering inside each round remains fixed regardless of the realizations seen inside the round. Our main result is that for any integer $r$, there exists a poly-time $r$-round adaptive algorithm for stochastic submodular cover whose expected cost is $\tilde{O}(Q^{{1}/{r}})$ times the expected cost of a fully adaptive algorithm. Prior to our work, such a result was not known even for the case of $r=1$ and when $f$ is the coverage function. On the other hand, we show that for any $r$, there exist instances of the stochastic submodular cover problem where no $r$-round adaptive algorithm can achieve better than $\Omega(Q^{{1}/{r}})$ approximation to the expected cost of a fully adaptive algorithm. Our lower bound result holds even for coverage function and for algorithms with unbounded computational power.

The problem of peer prediction is to elicit information from agents in settings without any objective ground truth against which to score reports. Peer prediction mechanisms seek to exploit correlations between signals to align incentives with truthful reports. A long-standing concern has been the possibility of uninformative equilibria. For binary signals, a multi-task mechanism [Dasgupta-Ghosh '13] achieves strong truthfulness, so that the truthful equilibrium strictly maximizes payoff. We characterize conditions on the signal distribution for which this mechanism remains strongly-truthful with non-binary signals, also providing a greatly simplified proof. We introduce the Correlated Agreement (CA) mechanism, which handles multiple signals and provides informed truthfulness: no strategy profile provides more payoff in equilibrium than truthful reporting, and the truthful equilibrium is strictly better than any uninformed strategy (where an agent avoids the effort of obtaining a signal). The CA mechanism is maximally strongly truthful, in that no mechanism in a broad class of mechanisms is strongly truthful on a larger family of signal distributions. We also give a detail-free version of the mechanism that removes any knowledge requirements on the part of the designer, using reports on many tasks to learn statistics while retaining epsilon-informed truthfulness.