Surprisingly Popular Voting for Concentric Rank-Order Models

An important problem on social information sites is the recovery of ground truth from individual reports when the experts are in the minority. The wisdom of the crowd, i.e. the collective opinion of a group of individuals fails in such a scenario. However, the surprisingly popular (SP) algorithm~\cite{prelec2017solution} can recover the ground truth even when the experts are in the minority, by asking the individuals to report additional prediction reports--their beliefs about the reports of others. Several recent works have extended the surprisingly popular algorithm to an equivalent voting rule (SP-voting) to recover the ground truth ranking over a set of $m$ alternatives. However, we are yet to fully understand when SP-voting can recover the ground truth ranking, and if so, how many samples (votes and predictions) it needs. We answer this question by proposing two rank-order models and analyzing the sample complexity of SP-voting under these models. In particular, we propose concentric mixtures of Mallows and Plackett-Luce models with $G (\ge 2)$ groups. Our models generalize previously proposed concentric mixtures of Mallows models with $2$ groups, and we highlight the importance of $G > 2$ groups by identifying three distinct groups (expert, intermediate, and non-expert) from existing datasets. Next, we provide conditions on the parameters of the underlying models so that SP-voting can recover ground-truth rankings with high probability, and also derive sample complexities under the same. We complement the theoretical results by evaluating SP-voting on simulated and real datasets.

Performative Reinforcement Learning with Linear Markov Decision Process

We study the setting of \emph{performative reinforcement learning} where the deployed policy affects both the reward, and the transition of the underlying Markov decision process. Prior work~\parencite{MTR23} has addressed this problem under the tabular setting and established last-iterate convergence of repeated retraining with iteration complexity explicitly depending on the number of states. In this work, we generalize the results to \emph{linear Markov decision processes} which is the primary theoretical model of large-scale MDPs. The main challenge with linear MDP is that the regularized objective is no longer strongly convex and we want a bound that scales with the dimension of the features, rather than states which can be infinite. Our first result shows that repeatedly optimizing a regularized objective converges to a \emph{performatively stable policy}. In the absence of strong convexity, our analysis leverages a new recurrence relation that uses a specific linear combination of optimal dual solutions for proving convergence. We then tackle the finite sample setting where the learner has access to a set of trajectories drawn from the current policy. We consider a reparametrized version of the primal problem, and construct an empirical Lagrangian which is to be optimized from the samples. We show that, under a \emph{bounded coverage} condition, repeatedly solving a saddle point of this empirical Lagrangian converges to a performatively stable solution, and also construct a primal-dual algorithm that solves the empirical Lagrangian efficiently. Finally, we show several applications of the general framework of performative RL including multi-agent systems.

Symmetric Linear Bandits with Hidden Symmetry

High-dimensional linear bandits with low-dimensional structure have received considerable attention in recent studies due to their practical significance. The most common structure in the literature is sparsity. However, it may not be available in practice. Symmetry, where the reward is invariant under certain groups of transformations on the set of arms, is another important inductive bias in the high-dimensional case that covers many standard structures, including sparsity. In this work, we study high-dimensional symmetric linear bandits where the symmetry is hidden from the learner, and the correct symmetry needs to be learned in an online setting. We examine the structure of a collection of hidden symmetry and provide a method based on model selection within the collection of low-dimensional subspaces. Our algorithm achieves a regret bound of $ O(d_0^{1/3} T^{2/3} \log(d))$, where $d$ is the ambient dimension which is potentially very large, and $d_0$ is the dimension of the true low-dimensional subspace such that $d_0 \ll d$. With an extra assumption on well-separated models, we can further improve the regret to $ O(d_0\sqrt{T\log(d)} )$.

Corruption-Robust Offline Two-Player Zero-Sum Markov Games

We study data corruption robustness in offline two-player zero-sum Markov games. Given a dataset of realized trajectories of two players, an adversary is allowed to modify an $\epsilon$-fraction of it. The learner's goal is to identify an approximate Nash Equilibrium policy pair from the corrupted data. We consider this problem in linear Markov games under different degrees of data coverage and corruption. We start by providing an information-theoretic lower bound on the suboptimality gap of any learner. Next, we propose robust versions of the Pessimistic Minimax Value Iteration algorithm, both under coverage on the corrupted data and under coverage only on the clean data, and show that they achieve (near)-optimal suboptimality gap bounds with respect to $\epsilon$. We note that we are the first to provide such a characterization of the problem of learning approximate Nash Equilibrium policies in offline two-player zero-sum Markov games under data corruption.

Reward Model Learning vs. Direct Policy Optimization: A Comparative Analysis of Learning from Human Preferences

In this paper, we take a step towards a deeper understanding of learning from human preferences by systematically comparing the paradigm of reinforcement learning from human feedback (RLHF) with the recently proposed paradigm of direct preference optimization (DPO). We focus our attention on the class of loglinear policy parametrization and linear reward functions. In order to compare the two paradigms, we first derive minimax statistical bounds on the suboptimality gap induced by both RLHF and DPO, assuming access to an oracle that exactly solves the optimization problems. We provide a detailed discussion on the relative comparison between the two paradigms, simultaneously taking into account the sample size, policy and reward class dimensions, and the regularization temperature. Moreover, we extend our analysis to the approximate optimization setting and derive exponentially decaying convergence rates for both RLHF and DPO. Next, we analyze the setting where the ground-truth reward is not realizable and find that, while RLHF incurs a constant additional error, DPO retains its asymptotically decaying gap by just tuning the temperature accordingly. Finally, we extend our comparison to the Markov decision process setting, where we generalize our results with exact optimization. To the best of our knowledge, we are the first to provide such a comparative analysis for RLHF and DPO.

Performative Reinforcement Learning in Gradually Shifting Environments

When Reinforcement Learning (RL) agents are deployed in practice, they might impact their environment and change its dynamics. Ongoing research attempts to formally model this phenomenon and to analyze learning algorithms in these models. To this end, we propose a framework where the current environment depends on the deployed policy as well as its previous dynamics. This is a generalization of Performative RL (PRL) [Mandal et al., 2023]. Unlike PRL, our framework allows to model scenarios where the environment gradually adjusts to a deployed policy. We adapt two algorithms from the performative prediction literature to our setting and propose a novel algorithm called Mixed Delayed Repeated Retraining (MDRR). We provide conditions under which these algorithms converge and compare them using three metrics: number of retrainings, approximation guarantee, and number of samples per deployment. Unlike previous approaches, MDRR combines samples from multiple deployments in its training. This makes MDRR particularly suitable for scenarios where the environment's response strongly depends on its previous dynamics, which are common in practice. We experimentally compare the algorithms using a simulation-based testbed and our results show that MDRR converges significantly faster than previous approaches.

Learning the Expected Core of Strictly Convex Stochastic Cooperative Games

Reward allocation, also known as the credit assignment problem, has been an important topic in economics, engineering, and machine learning. An important concept in credit assignment is the core, which is the set of stable allocations where no agent has the motivation to deviate from the grand coalition. In this paper, we consider the stable allocation learning problem of stochastic cooperative games, where the reward function is characterised as a random variable with an unknown distribution. Given an oracle that returns a stochastic reward for an enquired coalition each round, our goal is to learn the expected core, that is, the set of allocations that are stable in expectation. Within the class of strictly convex games, we present an algorithm named \texttt{Common-Points-Picking} that returns a stable allocation given a polynomial number of samples, with high probability. The analysis of our algorithm involves the development of several new results in convex geometry, including an extension of the separation hyperplane theorem for multiple convex sets, and may be of independent interest.

Corruption Robust Offline Reinforcement Learning with Human Feedback

We study data corruption robustness for reinforcement learning with human feedback (RLHF) in an offline setting. Given an offline dataset of pairs of trajectories along with feedback about human preferences, an $\varepsilon$-fraction of the pairs is corrupted (e.g., feedback flipped or trajectory features manipulated), capturing an adversarial attack or noisy human preferences. We aim to design algorithms that identify a near-optimal policy from the corrupted data, with provable guarantees. Existing theoretical works have separately studied the settings of corruption robust RL (learning from scalar rewards directly under corruption) and offline RLHF (learning from human feedback without corruption); however, they are inapplicable to our problem of dealing with corrupted data in offline RLHF setting. To this end, we design novel corruption robust offline RLHF methods under various assumptions on the coverage of the data-generating distributions. At a high level, our methodology robustifies an offline RLHF framework by first learning a reward model along with confidence sets and then learning a pessimistic optimal policy over the confidence set. Our key insight is that learning optimal policy can be done by leveraging an offline corruption-robust RL oracle in different ways (e.g., zero-order oracle or first-order oracle), depending on the data coverage assumptions. To our knowledge, ours is the first work that provides provable corruption robust offline RLHF methods.

Agent-Specific Effects

Establishing causal relationships between actions and outcomes is fundamental for accountable multi-agent decision-making. However, interpreting and quantifying agents' contributions to such relationships pose significant challenges. These challenges are particularly prominent in the context of multi-agent sequential decision-making, where the causal effect of an agent's action on the outcome depends on how the other agents respond to that action. In this paper, our objective is to present a systematic approach for attributing the causal effects of agents' actions to the influence they exert on other agents. Focusing on multi-agent Markov decision processes, we introduce agent-specific effects (ASE), a novel causal quantity that measures the effect of an agent's action on the outcome that propagates through other agents. We then turn to the counterfactual counterpart of ASE (cf-ASE), provide a sufficient set of conditions for identifying cf-ASE, and propose a practical sampling-based algorithm for estimating it. Finally, we experimentally evaluate the utility of cf-ASE through a simulation-based testbed, which includes a sepsis management environment.

Markov Decision Processes with Time-Varying Geometric Discounting

Canonical models of Markov decision processes (MDPs) usually consider geometric discounting based on a constant discount factor. While this standard modeling approach has led to many elegant results, some recent studies indicate the necessity of modeling time-varying discounting in certain applications. This paper studies a model of infinite-horizon MDPs with time-varying discount factors. We take a game-theoretic perspective -- whereby each time step is treated as an independent decision maker with their own (fixed) discount factor -- and we study the subgame perfect equilibrium (SPE) of the resulting game as well as the related algorithmic problems. We present a constructive proof of the existence of an SPE and demonstrate the EXPTIME-hardness of computing an SPE. We also turn to the approximate notion of $\epsilon$-SPE and show that an $\epsilon$-SPE exists under milder assumptions. An algorithm is presented to compute an $\epsilon$-SPE, of which an upper bound of the time complexity, as a function of the convergence property of the time-varying discount factor, is provided.