arXiv subjects

Debmalya Mandal

Publications and source records attributed to Debmalya Mandal.

At least 19 recordsLinked to original sources

arXiv2026

Inference-Time Nash Alignment

Preference-based fine-tuning methods such as RLHF and DPO require substantial compute and large preference datasets. They also need direct access to the model parameters which are not provided by many state-of-the art models. Inference-time alignment offers a cost-effective alternative without updating model parameters. However, existing inference-time methods rely on a scalar reward model derived under a Bradley-Terry assumption, which cannot represent general preferences. Following recent work on fine-tuning with generalized preferences, in this work, we initiate the study of inference-time alignment under general preferences. We formulate the problem as obtaining a Nash equilibrium of a two-player zero-sum game between policies. We propose two algorithms: Best-of-Nash (BoN) and Nash Mirror Descent (NMD). We prove that both algorithms achieve a duality gap that matches the problem lower bound. Empirically, we implement the two methods on three datasets, which shows that our methods substantially outperform the base policy, converging to the performance of the fine-tuned models. Moreover, our results show that NMD remains robust across the regularization parameter.

cs.AI↗

arXiv2026

Local and Global Stability in Performative Reinforcement Learning

In performative reinforcement learning the deployed policy shapes the environment that generates the learner's future data, and the natural solution concept is a performatively stable policy that is optimal in the environment it induces. Existing convergence guarantees rely on Lipschitz sensitivity assumptions on the environment map $\pi \mapsto (P_\pi, r_\pi)$, which are hard to verify and fail in settings such as multi-agent best-response dynamics. We instead study stability for mixtures of policies, and show that the resulting picture is fundamentally different from performative prediction, where randomization removes the need for any sensitivity assumption. We distinguish local mixed stability, an occupancy-weighted first-order relaxation that we show is equivalent to stationarity, from global mixed stability, which certifies against arbitrary deviating policies. Our first result is that a weighted per-state Hedge dynamic drives the local stability gap to zero at an $O(1/\sqrt{T})$ rate for an arbitrary, possibly discontinuous, environment map, both with exact and with trajectory feedback. The two notions genuinely differ: we exhibit an instance where local stability is achieved exactly but every mixture has global stability gap bounded away from zero. For global stability we introduce a bounded transition range assumption, strictly weaker than Lipschitz sensitivity, under which unweighted per-state Hedge converges up to a floor of $O(\gamma\epsilon_P/(1-\gamma)^3)$, and we prove a matching-in-$\epsilon_P$ lower bound of $\Omega(\gamma\epsilon_P/(1-\gamma))$ under trajectory feedback, so this floor is unavoidable. Finally, we extend both notions to $n$-player performative Markov games, obtaining local stability with no assumption on the joint environment map or game structure, and global stability for performative Markov potential games.

cs.LG↗

arXiv2026

Meta-Learning Preferences for Multilingual LLM Alignment

Unequal availability of human preference data across languages poses a significant challenge for aligning large language models in multilingual settings. To address the lack of sufficient data in low-resource language alignment, we propose a meta-learning framework for Reinforcement Learning from Human Feedback and Direct Preference Optimization. By leveraging preference data from other languages, our framework learns a transferable initialization that enables effective adaptation to a target language with minimal data. We provide theoretical guarantees for both the meta-reward modeling and meta-policy optimization settings, and empirically demonstrate the effectiveness of our approach on multilingual benchmarks. In an extremely low-resource setting with only 100 target-language preference samples, our approach achieves up to $28\%$ win-rate improvements over baseline methods, and consistently outperforms baselines across multiple target languages and model scales. Our approaches retain these advantages across different combinations of meta-training languages and varying linguistic distances from the target languages.

cs.CL↗

arXiv2026

Sparse Offline Reinforcement Learning with Corruption Robustness

We investigate robustness to strong data corruption in offline sparse reinforcement learning (RL). In our setting, an adversary may arbitrarily perturb a fraction of the collected trajectories from a high-dimensional but sparse Markov decision process, and our goal is to estimate a near optimal policy. The main challenge is that, in the high-dimensional regime where the number of samples $N$ is smaller than the feature dimension $d$, exploiting sparsity is essential for obtaining non-vacuous guarantees but has not been systematically studied in offline RL. We analyse the problem under uniform coverage and sparse single-concentrability assumptions. While Least Square Value Iteration (LSVI), a standard approach for robust offline RL, performs well under uniform coverage, we show that integrating sparsity into LSVI is unnatural, and its analysis may break down due to overly pessimistic bonuses. To overcome this, we propose actor-critic methods with sparse robust estimator oracles, which avoid the use of pointwise pessimistic bonuses and provide the first non-vacuous guarantees for sparse offline RL under single-policy concentrability coverage. Moreover, we extend our results to the contaminated setting and show that our algorithm remains robust under strong contamination. Our results provide the first non-vacuous guarantees in high-dimensional sparse MDPs with single-policy concentrability coverage and corruption, showing that learning a near-optimal policy remains possible in regimes where traditional robust offline RL techniques may fail.

stat.ML↗

arXiv2026

GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs

Conformal prediction (CP) provides a distribution-free approach to uncertainty quantification with finite-sample guarantees. However, applying CP to graph neural networks (GNNs) remains challenging as the combinatorial nature of graphs often leads to insufficiently certain predictions and indiscriminative embeddings. Existing methods primarily rely on embedding-space proximity for localization, which can be unreliable for graphs and yield inefficient prediction sets. We propose GRAPHLCP, a proximity-based localized CP framework that explicitly incorporates graph topology and inter-node dependencies into localization and weighting. Our approach introduces a feature-aware densification step to mitigate locality bias in sparse graphs, followed by a Personalized PageRank-based kernel computation to model structural proximity. This enables topology-dependent anchor sampling and calibration weighting that captures both local and long-range dependencies. Extensive experiments on several regression and classification datasets demonstrate that GRAPHLCP guarantees marginal coverage with finite samples while efficiently attaining favorable test conditional coverage across various conditioning scenarios.

cs.LG↗

arXiv2026

Corruption-robust Offline Multi-agent Reinforcement Learning From Human Feedback

We consider robustness against data corruption in offline multi-agent reinforcement learning from human feedback (MARLHF) under a strong-contamination model: given a dataset $D$ of trajectory-preference tuples (each preference being an $n$-dimensional binary label vector representing each of the $n$ agents' preferences), an $ε$-fraction of the samples may be arbitrarily corrupted. We model the problem using the framework of linear Markov games. First, under a uniform coverage assumption - where every policy of interest is sufficiently represented in the clean (prior to corruption) data - we introduce a robust estimator that guarantees an $O(ε^{1 - o(1)})$ bound on the Nash equilibrium gap. Next, we move to the more challenging unilateral coverage setting, in which only a Nash equilibrium and its single-player deviations are covered. In this case, our proposed algorithm achieves an $O(\sqrtε)$ bound on the Nash gap. Both of these procedures, however, suffer from intractable computation. To address this, we relax our solution concept to coarse correlated equilibria (CCE). Under the same unilateral coverage regime, we derive a quasi-polynomial-time algorithm whose CCE gap scales as $O(\sqrtε)$. To the best of our knowledge, this is the first systematic treatment of adversarial data corruption in offline MARLHF.

cs.LG↗

arXiv2025

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^{2/3} 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)} )$.

stat.ML↗

arXiv2025

SP-Rank: A Dataset for Ranked Preferences with Secondary Information

We introduce $\mathbf{SP-Rank}$, the first large-scale, publicly available dataset for benchmarking algorithms that leverage both first-order preferences and second-order predictions in ranking tasks. Each datapoint includes a personal vote (first-order signal) and a meta-prediction of how others will vote (second-order signal), allowing richer modeling than traditional datasets that capture only individual preferences. SP-Rank contains over 12,000 human-generated datapoints across three domains -- geography, movies, and paintings, and spans nine elicitation formats with varying subset sizes. This structure enables empirical analysis of preference aggregation when expert identities are unknown but presumed to exist, and individual votes represent noisy estimates of a shared ground-truth ranking. We benchmark SP-Rank by comparing traditional aggregation methods that use only first-order votes against SP-Voting, a second-order method that jointly reasons over both signals to infer ground-truth rankings. While SP-Rank also supports models that rely solely on second-order predictions, our benchmarks emphasize the gains from combining both signals. We evaluate performance across three core tasks: (1) full ground-truth rank recovery, (2) subset-level rank recovery, and (3) probabilistic modeling of voter behavior. Results show that incorporating second-order signals substantially improves accuracy over vote-only methods. Beyond social choice, SP-Rank supports downstream applications in learning-to-rank, extracting expert knowledge from noisy crowds, and training reward models in preference-based fine-tuning pipelines. We release the dataset, code, and baseline evaluations (available at https://github.com/amrit19/SP-Rank-Dataset ) to foster research in human preference modeling, aggregation theory, and human-AI alignment.

cs.IR↗

arXiv2025

Strategyproof Reinforcement Learning from Human Feedback

We study Reinforcement Learning from Human Feedback (RLHF) in settings where multiple labelers may strategically misreport feedback to steer the learned policy toward their own preferences. We show that existing RLHF algorithms, including recent pluralistic methods, are not strategyproof, and that even a single strategic labeler can cause arbitrarily large misalignment with social welfare. Moreover, we prove that, in the worst case, any strategyproof RLHF algorithm must perform $k$-times worse than the optimal policy, where $k$ is the number of labelers. This suggests a fundamental trade-off between incentive alignment (ensuring labelers report truthfully) and policy alignment (maximizing social welfare). To address this, we propose the Pessimistic Median of MLEs algorithm, which, under appropriate policy coverage assumptions, is approximately strategyproof and converges to the optimal policy as the number of labelers and samples increases. Our results apply to both contextual bandits and Markov decision processes.

cs.LG↗

arXiv2025

On Corruption-Robustness in Performative Reinforcement Learning

In performative Reinforcement Learning (RL), an agent faces a policy-dependent environment: the reward and transition functions depend on the agent's policy. Prior work on performative RL has studied the convergence of repeated retraining approaches to a performatively stable policy. In the finite sample regime, these approaches repeatedly solve for a saddle point of a convex-concave objective, which estimates the Lagrangian of a regularized version of the reinforcement learning problem. In this paper, we aim to extend such repeated retraining approaches, enabling them to operate under corrupted data. More specifically, we consider Huber's $ε$-contamination model, where an $ε$ fraction of data points is corrupted by arbitrary adversarial noise. We propose a repeated retraining approach based on convex-concave optimization under corrupted gradients and a novel problem-specific robust mean estimator for the gradients. We prove that our approach exhibits last-iterate convergence to an approximately stable policy, with the approximation error linear in $\sqrtε$. We experimentally demonstrate the importance of accounting for corruption in performative RL.

cs.LG↗

arXiv2025

Independent Learning in Performative Markov Potential Games

Performative Reinforcement Learning (PRL) refers to a scenario in which the deployed policy changes the reward and transition dynamics of the underlying environment. In this work, we study multi-agent PRL by incorporating performative effects into Markov Potential Games (MPGs). We introduce the notion of a performatively stable equilibrium (PSE) and show that it always exists under a reasonable sensitivity assumption. We then provide convergence results for state-of-the-art algorithms used to solve MPGs. Specifically, we show that independent policy gradient ascent (IPGA) and independent natural policy gradient (INPG) converge to an approximate PSE in the best-iterate sense, with an additional term that accounts for the performative effects. Furthermore, we show that INPG asymptotically converges to a PSE in the last-iterate sense. As the performative effects vanish, we recover the convergence rates from prior work. For a special case of our game, we provide finite-time last-iterate convergence results for a repeated retraining approach, in which agents independently optimize a surrogate objective. We conduct extensive experiments to validate our theoretical findings.

cs.LG↗

arXiv2025

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.

cs.LG↗

arXiv2025

Policy Teaching via Data Poisoning in Learning from Human Preferences

We study data poisoning attacks in learning from human preferences. More specifically, we consider the problem of teaching/enforcing a target policy $π^\dagger$ by synthesizing preference data. We seek to understand the susceptibility of different preference-based learning paradigms to poisoned preference data by analyzing the number of samples required by the attacker to enforce $π^\dagger$. We first propose a general data poisoning formulation in learning from human preferences and then study it for two popular paradigms, namely: (a) reinforcement learning from human feedback (RLHF) that operates by learning a reward model using preferences; (b) direct preference optimization (DPO) that directly optimizes policy using preferences. We conduct a theoretical analysis of the effectiveness of data poisoning in a setting where the attacker is allowed to augment a pre-existing dataset and also study its special case where the attacker can synthesize the entire preference dataset from scratch. As our main results, we provide lower/upper bounds on the number of samples required to enforce $π^\dagger$. Finally, we discuss the implications of our results in terms of the susceptibility of these learning paradigms under such data poisoning attacks.

cs.LG↗

arXiv2025

Distributionally Robust Reinforcement Learning with Human Feedback

Reinforcement learning from human feedback (RLHF) has evolved to be one of the main methods for fine-tuning large language models (LLMs). However, existing RLHF methods are non-robust, and their performance deteriorates if the downstream task differs significantly from the preference dataset used in fine-tuning. In order to mitigate this problem, we introduce a distributionally robust RLHF for fine-tuning LLMs. In particular, our goal is to ensure that a fine-tuned model retains its performance even when the distribution of prompts significantly differs from the distribution encountered during fine-tuning. We formulate distributionally robust optimization (DRO) version of two popular fine-tuning methods -- (1) reward-based RLHF and (2) reward-free DPO (direct preference optimization). We propose a minibatch gradient descent based algorithms for both of them, and theoretically prove convergence guarantees for the algorithms. Subsequently, we evaluate our algorithms on an out-of-distribution (OOD) task by first training the model on the Unified-Feedback dataset and evaluating its performance on two different datasets. The experimental results show that our robust training improves the accuracy of the learned reward models on average, and markedly on some tasks, such as reasoning. Furthermore, we show that the robust versions of policy optimization methods, similarly improve performance on OOD tasks.

cs.LG↗

arXiv2024

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.

cs.GT↗

arXiv2024

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 reward allocation is the core, which is the set of stable allocations where no agent has the motivation to deviate from the grand coalition. In previous works, computing the core requires either knowledge of the reward function in deterministic games or the reward distribution in stochastic games. However, this is unrealistic, as the reward function or distribution is often only partially known and may be subject to uncertainty. In this paper, we consider the core learning problem in stochastic cooperative games, where the reward distribution is unknown. Our goal is to learn the expected core, that is, the set of allocations that are stable in expectation, given an oracle that returns a stochastic reward for an enquired coalition each round. Within the class of strictly convex games, we present an algorithm named \texttt{Common-Points-Picking} that returns a point in the expected core given a polynomial number of samples, with high probability. To analyse the algorithm, we develop a new extension of the separation hyperplane theorem for multiple convex sets.

cs.GT↗

arXiv2024

Stochastic Principal-Agent Problems: Efficient Computation and Learning

We introduce a stochastic principal-agent model. A principal and an agent interact in a stochastic environment, each privy to observations about the state not available to the other. The principal has the power of commitment, both to elicit information from the agent and to provide signals about her own information. The players communicate with each other and then select actions independently. Each of them receives a payoff based on the state and their joint action, and the environment transitions to a new state. The interaction continues over a finite time horizon. Both players are far-sighted, aiming to maximize their total payoffs over the time horizon. The model encompasses as special cases extensive-form games (EFGs) and stochastic games of incomplete information, partially observable Markov decision processes (POMDPs), as well as other forms of sequential principal-agent interactions, including Bayesian persuasion and automated mechanism design problems. We consider both the computation and learning of the principal's optimal policy. Since the general problem, which subsumes POMDPs, is intractable, we explore algorithmic solutions under hindsight observability, where the state and the interaction history are revealed at the end of each step. Though the problem becomes more amenable under this condition, the number of possible histories remains exponential in the length of the time horizon, making approaches for EFG-based models infeasible. We present an efficient algorithm based on the inducible value sets. The algorithm computes an $ε$-approximate optimal policy in time polynomial in $1/ε$. Additionally, we show an efficient learning algorithm for an episodic reinforcement learning setting where the transition probabilities are unknown. The algorithm guarantees sublinear regret $\tilde{O}(T^{2/3})$ for both players over $T$ episodes.

cs.GT↗

arXiv2024

Agent-Specific Effects: A Causal Effect Propagation Analysis in Multi-Agent MDPs

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 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.

cs.AI↗