arXiv subjects

Sujay Bhatt

Publications and source records attributed to Sujay Bhatt.

At least 19 recordsLinked to original sources

arXiv2026

Rethinking Neural Network Learning Rates: A Stackelberg Perspective

Neural networks are typically trained with a single learning rate across all layers. While recent empirical evidence suggests that assigning layer-specific learning rates can accelerate training, a principled understanding of the conditions and mechanisms under which non-uniform learning rates are beneficial remains limited. In this work, we investigate non-uniform learning rates through the lens of Stackelberg optimization. Specifically, we demonstrate that training neural networks with a smaller learning rate for the body layers and a larger learning rate for the final layer can be interpreted as a two-time-scale alternating gradient descent algorithm applied to a Stackelberg reformulation of the original objective. We establish finite-time convergence guarantees for the algorithm under broad conditions that accommodate constraint sets and non-smooth activation functions. Beyond convergence, we identify two mechanisms by which non-uniform learning rates can outperform uniform learning rates: (i) we show that certain problem instances induce a Stackelberg objective with stronger optimization structure than the original objective, yielding faster convergence to globally optimal solutions, (ii) our numerical analysis reveals that the Stackelberg objective can exhibit substantially sharper local curvature, especially in early training, which leads to more informative gradients and learning acceleration. Experiments in supervised learning and reinforcement learning support our findings.

cs.LG↗

arXiv2026

A Hessian-Free Actor-Critic Algorithm for Bi-Level Reinforcement Learning with Applications to LLM Fine-Tuning

We study a structured bi-level optimization problem where the upper-level objective is a smooth function and the lower-level problem is policy optimization in a Markov decision process (MDP). The upper-level decision variable parameterizes the reward of the lower-level MDP, and the upper-level objective depends on the optimal induced policy. Existing methods for bi-level optimization and RL often require second-order information, impose strong regularization at the lower level, or inefficiently use samples through nested-loop procedures. In this work, we propose a single-loop, first-order actor-critic algorithm that optimizes the bi-level objective via a penalty-based reformulation. We introduce into the lower-level RL objective an attenuating entropy regularization, which enables asymptotically unbiased upper-level hyper-gradient estimation without solving the unregularized RL problem exactly. We establish the finite-time and finite-sample convergence of the proposed algorithm to a stationary point of the original, unregularized bi-level optimization problem through a novel lower-level residual analysis under a special type of Polyak-Lojasiewicz condition. We validate the performance of our method through experiments on a GridWorld goal position problem and on happy tweet generation through reinforcement learning from human feedback (RLHF).

cs.LG↗

arXiv2025

Learning in Stackelberg Mean Field Games: A Non-Asymptotic Analysis

We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

cs.LG↗

arXiv2025

Catoni-Style Change Point Detection for Regret Minimization in Non-Stationary Heavy-Tailed Bandits

Regret minimization in stochastic non-stationary bandits gained popularity over the last decade, as it can model a broad class of real-world problems, from advertising to recommendation systems. Existing literature relies on various assumptions about the reward-generating process, such as Bernoulli or subgaussian rewards. However, in settings such as finance and telecommunications, heavy-tailed distributions naturally arise. In this work, we tackle the heavy-tailed piecewise-stationary bandit problem. Heavy-tailed bandits, introduced by Bubeck et al., 2013, operate on the minimal assumption that the finite absolute centered moments of maximum order $1+\epsilon$ are uniformly bounded by a constant $v<+\infty$, for some $\epsilon \in (0,1]$. We focus on the most popular non-stationary bandit setting, i.e., the piecewise-stationary setting, in which the mean of reward-generating distributions may change at unknown time steps. We provide a novel Catoni-style change-point detection strategy tailored for heavy-tailed distributions that relies on recent advancements in the theory of sequential estimation, which is of independent interest. We introduce Robust-CPD-UCB, which combines this change-point detection strategy with optimistic algorithms for bandits, providing its regret upper bound and an impossibility result on the minimum attainable regret for any policy. Finally, we validate our approach through numerical experiments on synthetic and real-world datasets.

cs.LG↗

arXiv2025

Collab: Controlled Decoding using Mixture of Agents for LLM Alignment

Alignment of Large Language models (LLMs) is crucial for safe and trustworthy deployment in applications. Reinforcement learning from human feedback (RLHF) has emerged as an effective technique to align LLMs to human preferences and broader utilities, but it requires updating billions of model parameters, which is computationally expensive. Controlled Decoding, by contrast, provides a mechanism for aligning a model at inference time without retraining. However, single-agent decoding approaches often struggle to adapt to diverse tasks due to the complexity and variability inherent in these tasks. To strengthen the test-time performance w.r.t the target task, we propose a mixture of agent-based decoding strategies leveraging the existing off-the-shelf aligned LLM policies. Treating each prior policy as an agent in the spirit of mixture of agent collaboration, we develop a decoding method that allows for inference-time alignment through a token-level selection strategy among multiple agents. For each token, the most suitable LLM is dynamically chosen from a pool of models based on a long-term utility metric. This policy-switching mechanism ensures optimal model selection at each step, enabling efficient collaboration and alignment among LLMs during decoding. Theoretical analysis of our proposed algorithm establishes optimal performance with respect to the target task represented via a target reward for the given off-the-shelf models. We conduct comprehensive empirical evaluations with open-source aligned models on diverse tasks and preferences, which demonstrates the merits of this approach over single-agent decoding baselines. Notably, Collab surpasses the current SoTA decoding strategy, achieving an improvement of up to 1.56x in average reward and 71.89% in GPT-4 based win-tie rate.

cs.CL↗

arXiv2025

Regularized Proportional Fairness Mechanism for Resource Allocation Without Money

Mechanism design in resource allocation studies dividing limited resources among self-interested agents whose satisfaction with the allocation depends on privately held utilities. We consider the problem in a payment-free setting, with the aim of maximizing social welfare while enforcing incentive compatibility (IC), i.e., agents cannot inflate allocations by misreporting their utilities. The well-known proportional fairness (PF) mechanism achieves the maximum possible social welfare but incurs an undesirably high exploitability (the maximum unilateral inflation in utility from misreport and a measure of deviation from IC). In fact, it is known that no mechanism can achieve the maximum social welfare and exact incentive compatibility (IC) simultaneously without the use of monetary incentives (Cole et al., 2013). Motivated by this fact, we propose learning an approximate mechanism that desirably trades off the competing objectives. Our main contribution is to design an innovative neural network architecture tailored to the resource allocation problem, which we name Regularized Proportional Fairness Network (RPF-Net). RPF-Net regularizes the output of the PF mechanism by a learned function approximator of the most exploitable allocation, with the aim of reducing the incentive for any agent to misreport. We derive generalization bounds that guarantee the mechanism performance when trained under finite and out-of-distribution samples and experimentally demonstrate the merits of the proposed mechanism compared to the state-of-the-art.

cs.GT↗

arXiv2024

Decentralized Convergence to Equilibrium Prices in Trading Networks

We propose a decentralized market model in which agents can negotiate bilateral contracts. This builds on a similar, but centralized, model of trading networks introduced by Hatfield et al. in 2013. Prior work has established that fully-substitutable preferences guarantee the existence of competitive equilibria which can be centrally computed. Our motivation comes from the fact that prices in markets such as over-the-counter markets and used car markets arise from decentralized negotiation among agents, which has left open an important question as to whether equilibrium prices can emerge from agent-to-agent bilateral negotiations. We design a best response dynamic intended to capture such negotiations between market participants. We assume fully substitutable preferences for market participants. In this setting, we provide proofs of convergence for sparse markets (covering many real world markets of interest), and experimental results for more general cases, demonstrating that prices indeed reach equilibrium, quickly, via bilateral negotiations. Our best response dynamic, and its convergence behavior, forms an important first step in understanding how decentralized markets reach, and retain, equilibrium.

cs.GT↗

arXiv2024

Approximate Equivariance in Reinforcement Learning

Equivariant neural networks have shown great success in reinforcement learning, improving sample efficiency and generalization when there is symmetry in the task. However, in many problems, only approximate symmetry is present, which makes imposing exact symmetry inappropriate. Recently, approximately equivariant networks have been proposed for supervised classification and modeling physical systems. In this work, we develop approximately equivariant algorithms in reinforcement learning (RL). We define approximately equivariant MDPs and theoretically characterize the effect of approximate equivariance on the optimal $Q$ function. We propose novel RL architectures using relaxed group and steerable convolutions and experiment on several continuous control domains and stock trading with real financial data. Our results demonstrate that the approximately equivariant network performs on par with exactly equivariant networks when exact symmetries are present, and outperforms them when the domains exhibit approximate symmetry. As an added byproduct of these techniques, we observe increased robustness to noise at test time. Our code is available at https://github.com/jypark0/approx_equiv_rl.

cs.LG↗

arXiv2024

Partially Observable Contextual Bandits with Linear Payoffs

The standard contextual bandit framework assumes fully observable and actionable contexts. In this work, we consider a new bandit setting with partially observable, correlated contexts and linear payoffs, motivated by the applications in finance where decision making is based on market information that typically displays temporal correlation and is not fully observed. We make the following contributions marrying ideas from statistical signal processing with bandits: (i) We propose an algorithmic pipeline named EMKF-Bandit, which integrates system identification, filtering, and classic contextual bandit algorithms into an iterative method alternating between latent parameter estimation and decision making. (ii) We analyze EMKF-Bandit when we select Thompson sampling as the bandit algorithm and show that it incurs a sub-linear regret under conditions on filtering. (iii) We conduct numerical simulations that demonstrate the benefits and practical applicability of the proposed pipeline.

cs.LG↗

arXiv2024

Learning in Herding Mean Field Games: Single-Loop Algorithm with Finite-Time Convergence Analysis

We consider discrete-time stationary mean field games (MFG) with unknown dynamics and design algorithms for finding the equilibrium with finite-time complexity guarantees. Prior solutions to the problem assume either the contraction of a mean field optimality-consistency operator or strict weak monotonicity, which may be overly restrictive. In this work, we introduce a new class of solvable MFGs, named the "fully herding class", which expands the known solvable class of MFGs and for the first time includes problems with multiple equilibria. We propose a direct policy optimization method, Accelerated Single-loop Actor Critic Algorithm for Mean Field Games (ASAC-MFG), that provably finds a global equilibrium for MFGs within this class, under suitable access to a single trajectory of Markovian samples. Different from the prior methods, ASAC-MFG is single-loop and single-sample-path. We establish the finite-time and finite-sample convergence of ASAC-MFG to a mean field equilibrium via new techniques that we develop for multi-time-scale stochastic approximation. We support the theoretical results with illustrative numerical simulations. When the mean field does not affect the transition and reward, a MFG reduces to a Markov decision process (MDP) and ASAC-MFG becomes an actor-critic algorithm for finding the optimal policy in average-reward MDPs, with a sample complexity matching the state-of-the-art. Previous works derive the complexity assuming a contraction on the Bellman operator, which is invalid for average-reward MDPs. We match the rate while removing the untenable assumption through an improved Lyapunov function.

math.OC↗

arXiv2023

Learning Payment-Free Resource Allocation Mechanisms

We consider the design of mechanisms that allocate limited resources among self-interested agents using neural networks. Unlike the recent works that leverage machine learning for revenue maximization in auctions, we consider welfare maximization as the key objective in the payment-free setting. Without payment exchange, it is unclear how we can align agents' incentives to achieve the desired objectives of truthfulness and social welfare simultaneously, without resorting to approximations. Our work makes novel contributions by designing an approximate mechanism that desirably trade-off social welfare with truthfulness. Specifically, (i) we contribute a new end-to-end neural network architecture, ExS-Net, that accommodates the idea of "money-burning" for mechanism design without payments; (ii)~we provide a generalization bound that guarantees the mechanism performance when trained under finite samples; and (iii) we provide an experimental demonstration of the merits of the proposed mechanism.

cs.GT↗

arXiv2022

Oracle-free Reinforcement Learning in Mean-Field Games along a Single Sample Path

We consider online reinforcement learning in Mean-Field Games (MFGs). Unlike traditional approaches, we alleviate the need for a mean-field oracle by developing an algorithm that approximates the Mean-Field Equilibrium (MFE) using the single sample path of the generic agent. We call this {\it Sandbox Learning}, as it can be used as a warm-start for any agent learning in a multi-agent non-cooperative setting. We adopt a two time-scale approach in which an online fixed-point recursion for the mean-field operates on a slower time-scale, in tandem with a control policy update on a faster time-scale for the generic agent. Given that the underlying Markov Decision Process (MDP) of the agent is communicating, we provide finite sample convergence guarantees in terms of convergence of the mean-field and control policy to the mean-field equilibrium. The sample complexity of the Sandbox learning algorithm is $\tilde{\mathcal{O}}(\epsilon^{-4})$ where $\epsilon$ is the MFE approximation error. This is similar to works which assume access to oracle. Finally, we empirically demonstrate the effectiveness of the sandbox learning algorithm in diverse scenarios, including those where the MDP does not necessarily have a single communicating class.

cs.LG↗

arXiv2022

Catoni-style Confidence Sequences under Infinite Variance

In this paper, we provide an extension of confidence sequences for settings where the variance of the data-generating distribution does not exist or is infinite. Confidence sequences furnish confidence intervals that are valid at arbitrary data-dependent stopping times, naturally having a wide range of applications. We first establish a lower bound for the width of the Catoni-style confidence sequences for the finite variance case to highlight the looseness of the existing results. Next, we derive tight Catoni-style confidence sequences for data distributions having a relaxed bounded~$p^{th}-$moment, where~$p \in (1,2]$, and strengthen the results for the finite variance case of~$p =2$. The derived results are shown to better than confidence sequences obtained using Dubins-Savage inequality.

math.ST↗

arXiv2022

Offline Change Detection under Contamination

In this work, we propose a non-parametric and robust change detection algorithm to detect multiple change points in time series data under contamination. The contamination model is sufficiently general, in that, the most common model used in the context of change detection -- Huber contamination model -- is a special case. Also, the contamination model is oblivious and arbitrary. The change detection algorithm is designed for the offline setting, where the objective is to detect changes when all data are received. We only make weak moment assumptions on the inliers (uncorrupted data) to handle a large class of distributions. The robust scan statistic in the algorithm is fashioned using mean estimators based on influence functions. We establish the consistency of the estimated change point indexes as the number of samples increases, and provide empirical evidence to support the consistency results.

stat.ME↗

arXiv2021

Adversarial Linear-Quadratic Mean-Field Games over Multigraphs

In this paper, we propose a game between an exogenous adversary and a network of agents connected via a multigraph. The multigraph is composed of (1) a global graph structure, capturing the virtual interactions among the agents, and (2) a local graph structure, capturing physical/local interactions among the agents. The aim of each agent is to achieve consensus with the other agents in a decentralized manner by minimizing a local cost associated with its local graph and a global cost associated with the global graph. The exogenous adversary, on the other hand, aims to maximize the average cost incurred by all agents in the multigraph. We derive Nash equilibrium policies for the agents and the adversary in the Mean-Field Game setting, when the agent population in the global graph is arbitrarily large and the ``homogeneous mixing" hypothesis holds on local graphs. This equilibrium is shown to be unique and the equilibrium Markov policies for each agent depend on the local state of the agent, as well as the influences on the agent by the local and global mean fields.

eess.SY↗

arXiv2021

Extreme Bandits using Robust Statistics

We consider a multi-armed bandit problem motivated by situations where only the extreme values, as opposed to expected values in the classical bandit setting, are of interest. We propose distribution free algorithms using robust statistics and characterize the statistical properties. We show that the provided algorithms achieve vanishing extremal regret under weaker conditions than existing algorithms. Performance of the algorithms is demonstrated for the finite-sample setting using numerical experiments. The results show superior performance of the proposed algorithms compared to the well known algorithms.

stat.ML↗

arXiv2020

Policy Gradient using Weak Derivatives for Reinforcement Learning

This paper considers policy search in continuous state-action reinforcement learning problems. Typically, one computes search directions using a classic expression for the policy gradient called the Policy Gradient Theorem, which decomposes the gradient of the value function into two factors: the score function and the Q-function. This paper presents four results:(i) an alternative policy gradient theorem using weak (measure-valued) derivatives instead of score-function is established; (ii) the stochastic gradient estimates thus derived are shown to be unbiased and to yield algorithms that converge almost surely to stationary points of the non-convex value function of the reinforcement learning problem; (iii) the sample complexity of the algorithm is derived and is shown to be $O(1/\sqrt(k))$; (iv) finally, the expected variance of the gradient estimates obtained using weak derivatives is shown to be lower than those obtained using the popular score-function approach. Experiments on OpenAI gym pendulum environment show superior performance of the proposed algorithm.

cs.LG↗

arXiv2018

Adaptive Polling in Hierarchical Social Networks using Blackwell Dominance

Consider a population of individuals that observe an underlying state of nature that evolves over time. The population is classified into different levels depending on the hierarchical influence that dictates how the individuals at each level form an opinion on the state. The population is sampled sequentially by a pollster and the nodes (or individuals) respond to the questions asked by the pollster. This paper considers the following problem: How should the pollster poll the hierarchical social network to estimate the state while minimizing the polling cost (measurement cost and uncertainty in the Bayesian state estimate)? This paper proposes adaptive versions of the following polling methods: Intent Polling, Expectation Polling, and the recently proposed Neighbourhood Expectation Polling to account for the time varying state of nature and the hierarchical influence in social networks. The adaptive polling problem in a hierarchical social network is formulated as a partially observed Markov decision process (POMDP). Our main results exploit the structure of the polling problem, and determine novel conditions for Blackwell dominance to construct myopic policies that provably upper bound the optimal policy of the adaptive polling POMDP. The LeCam deficiency is used to determine approximate Blackwell dominance for general polling problems. These Blackwell dominance conditions also facilitate the comparison of Renyi Divergence and Shannon capacity of more general channel structures that arise in hierarchical social networks. Numerical examples are provided to illustrate the adaptive polling policies with parameters estimated from YouTube data.

cs.SI↗