arXiv subjects

Sayak Ray Chowdhury

Publications and source records attributed to Sayak Ray Chowdhury.

At least 19 recordsLinked to original sources

arXiv2026

Instruction Distillation: Text Instructions as Visual Examples

Visual in-context learning (ICL) with multimodal large language models (MLLMs) is effective for fine-grained visual classification, but each retrieved image example consumes several hundred context tokens, making large-$K$ settings prohibitively expensive at inference scale. We propose Instruction Distillation: an offline procedure in which the MLLM itself generates, for each individual training image, a structured identification instruction encoding general appearance cues, features that differentiate the class from visually similar ones, and a common confusion point. Unlike prior work that produces a single description per class, our instructions are generated per training image, preserving the intra-class visual diversity that per-class descriptions collapse. At inference time, we study five configurations sharing a single CLIP retrieval index: zero-shot, image ICL, instruction-only ICL, and two hybrid variants in which retrieved neighbors are split between images and instructions. Across seven fine-grained benchmarks and two MLLM backbones, instruction based pipelines match, or exceeds image ICL at $K{=}1$ and reduces per-query tokens by $2.9\times$ and inference latency by $3.3\times$ at $K{=}5$. Hybrid configurations further show that visual and textual ICL signals are complementary, images give visual patterns to learn and see, while instructions give explicit rules and logic. When both of these are provided, the quality of context improves, which is noticeable in the performance.

cs.CV↗

arXiv2026

Privacy Without Regret: Differentially Private Inference-Time Alignment

Best-of-N (BoN) sampling is the simplest and most widely deployed inference-time alignment strategy, but it suffers from two distinct problems: reward hacking, in which the selected response exploits errors in the proxy reward model, and the absence of any privacy protection for the sensitive human preference data used to train that reward model. We show that a single intervention-adding calibrated noise to reward scores before selection-resolves both. Our first result, Private Best-of-N (PrivBoN), establishes that Gumbel noise at an appropriate scale simultaneously provides $\epsilon$-differential privacy and implements KL-regularized alignment. Whenever the privacy budget exceeds a critical threshold $\epsilon^*$, the privacy-mandated noise is the regret-optimal regularization, and privacy imposes zero additional alignment cost-matching the information-theoretic skyline of Huang et al. (2025). Because $\epsilon^*$ depends on an unknown coverage coefficient, we introduce Private Inference-Time Pessimism (PrivITP), which combines $\chi^2$-regularized rejection sampling with a two-phase Gaussian mechanism. PrivITP achieves ex-post $(\epsilon,\delta)$-DP with a privacy cost independent of the number of responses $n$, cleanly decouples the regularization parameter from the privacy parameter, and attains the skyline up to a noise-inflation term. Experiments across several language models, datasets, and reward models confirm our results: PrivBoN and PrivITP are scaling-monotonic (unlike BoN, which degrades past a critical $n$), and PrivITP matches or outperforms PrivBoN at equivalent privacy levels, with the largest gains in the strong-privacy regime.

cs.LG↗

arXiv2026

Price of Fairness in Bandits: A Tight Minimax Characterization

In bandit problems, standard regret-minimizing algorithms treat exploration as an amortized cost, which can expose early participants to unfair ex-ante losses in settings such as clinical trials. Recent work addresses this by evaluating the sequence of per-round expected rewards through the generalized $p$-mean, interpolating between utilitarian welfare ($p=1$), Nash welfare ($p\to0$), and Rawlsian fairness ($p\to-\infty$). Although tight guarantees are known for $p\ge0$, the strictly fair regime $q=-p>0$ remains unresolved because negative-power means are dominated by the smallest per-round rewards. For $\sigma$-sub-Gaussian rewards with nonnegative means, the best prior algorithm relied on uniform early exploration and achieved regret $O(k^{(q+1)/2}/\sqrt{T})$, while the only general lower bound was the classical $\Omega(\sigma\sqrt{k/T})$. Thus it was unclear whether the extra dependence on $k$ was intrinsic to strict fairness or an artifact of uniform exploration. We close this gap by identifying the exact polynomial price of strict fairness. Using a needle-in-haystack construction, we prove an algorithm-independent lower bound $\Omega(\sigma\sqrt{k^{\max(1,q)}/T})$; for $q>1$, this shows that the penalty $k^{q/2}$ is information-theoretically unavoidable. We then introduce \textsf{UCB-HARE} (Harmonic Anchored Rank Exploration), which replaces uniform exploration with an inverse-weighted harmonic rank schedule protected by a certified positive-mean anchor. Its regret is $\widetilde{O}(\sigma\sqrt{k^{\max(1,q)}/T})$, matching the lower bound up to logarithmic factors. Experiments on synthetic instances confirm that \textsf{UCB-HARE} improves over uniform-exploration baselines, with gains increasing as $q$ grows.

stat.ML↗

arXiv2026

Improved Algorithms for Nash Welfare in Linear Bandits

Nash regret has recently emerged as a principled fairness-aware performance metric for stochastic multi-armed bandits, motivated by the Nash Social Welfare objective. Although this notion has been extended to linear bandits, existing results suffer from suboptimality in ambient dimension $d$, stemming from proof techniques that rely on restrictive concentration inequalities. In this work, we resolve this open problem by introducing new analytical tools that yield an order-optimal Nash regret bound in linear bandits. Beyond Nash regret, we initiate the study of $p$-means regret in linear bandits, a unifying framework that interpolates between fairness and utility objectives and strictly generalizes Nash regret. We propose a generic algorithmic framework, FairLinBandit, that works as a meta-algorithm on top of any linear bandit strategy. We instantiate this framework using two bandit algorithms: Phased Elimination and Upper Confidence Bound, and prove that both achieve sublinear $p$-means regret for the entire range of $p$. Extensive experiments on linear bandit instances generated from real-world datasets demonstrate that our methods consistently outperform the existing state-of-the-art baseline.

cs.LG↗

arXiv2026

Right Now, Wrong Then: Non-Stationary Direct Preference Optimization under Preference Drift

Current Large Language Model (LLM) preference optimization algorithms do not account for temporal preference drift, which can lead to severe misalignment. To address this limitation, we propose Non-Stationary Direct Preference Optimisation (NS-DPO) that models time-dependent reward functions with a Dynamic Bradley-Terry model. NS-DPO proposes a computationally efficient solution by introducing only a single discount parameter in the loss function, which is used for exponential weighting that proportionally focuses learning on more time-relevant datapoints. We theoretically analyze the convergence of NS-DPO in a general setting where the exact nature of the preference drift is not known, providing upper bounds on the estimation error and regret caused by non-stationary preferences. Finally, we demonstrate the effectiveness of NS-DPO for fine-tuning LLMs under drifting preferences. Using scenarios where various levels of preference drift is introduced, with popular LLM reward models and datasets, we show that NS-DPO fine-tuned LLMs remain robust under non-stationarity, significantly outperforming baseline algorithms that ignore temporal preference changes, without sacrificing performance in stationary cases.

cs.LG↗

arXiv2025

Revisiting Social Welfare in Bandits: UCB is (Nearly) All You Need

Regret in stochastic multi-armed bandits traditionally measures the difference between the highest reward and either the arithmetic mean of accumulated rewards or the final reward. These conventional metrics often fail to address fairness among agents receiving rewards, particularly in settings where rewards are distributed across a population, such as patients in clinical trials. To address this, a recent body of work has introduced Nash regret, which evaluates performance via the geometric mean of accumulated rewards, aligning with the Nash social welfare function known for satisfying fairness axioms. To minimize Nash regret, existing approaches require specialized algorithm designs and strong assumptions, such as multiplicative concentration inequalities and bounded, non-negative rewards, making them unsuitable for even Gaussian reward distributions. We demonstrate that an initial uniform exploration phase followed by a standard Upper Confidence Bound (UCB) algorithm achieves near-optimal Nash regret, while relying only on additive Hoeffding bounds, and naturally extending to sub-Gaussian rewards. Furthermore, we generalize the algorithm to a broad class of fairness metrics called the $p$-mean regret, proving (nearly) optimal regret bounds uniformly across all $p$ values. This is in contrast to prior work, which made extremely restrictive assumptions on the bandit instances and even then achieved suboptimal regret bounds.

cs.LG↗

arXiv2025

Why DPO is a Misspecified Estimator and How to Fix It

Direct alignment algorithms such as Direct Preference Optimization (DPO) fine-tune models based on preference data, using only supervised learning instead of two-stage reinforcement learning with human feedback (RLHF). We show that DPO encodes a statistical estimation problem over reward functions induced by a parametric policy class. When the true reward function that generates preferences cannot be realized via the policy class, DPO becomes misspecified, resulting in failure modes such as preference order reversal, worsening of policy reward, and high sensitivity to the input preference data distribution. On the other hand, we study the local behavior of two-stage RLHF for a parametric class and relate it to a natural gradient step in policy space. Our fine-grained geometric characterization allows us to propose AuxDPO, which introduces additional auxiliary variables in the DPO loss function to help move towards the RLHF solution in a principled manner and mitigate the misspecification in DPO. We empirically demonstrate the superior performance of AuxDPO on didactic bandit settings as well as LLM alignment tasks.

cs.LG↗

arXiv2025

Constrained Adversarial Perturbation

Deep neural networks have achieved remarkable success in a wide range of classification tasks. However, they remain highly susceptible to adversarial examples - inputs that are subtly perturbed to induce misclassification while appearing unchanged to humans. Among various attack strategies, Universal Adversarial Perturbations (UAPs) have emerged as a powerful tool for both stress testing model robustness and facilitating scalable adversarial training. Despite their effectiveness, most existing UAP methods neglect domain specific constraints that govern feature relationships. Violating such constraints, such as debt to income ratios in credit scoring or packet flow invariants in network communication, can render adversarial examples implausible or easily detectable, thereby limiting their real world applicability. In this work, we advance universal adversarial attacks to constrained feature spaces by formulating an augmented Lagrangian based min max optimization problem that enforces multiple, potentially complex constraints of varying importance. We propose Constrained Adversarial Perturbation (CAP), an efficient algorithm that solves this problem using a gradient based alternating optimization strategy. We evaluate CAP across diverse domains including finance, IT networks, and cyber physical systems, and demonstrate that it achieves higher attack success rates while significantly reducing runtime compared to existing baselines. Our approach also generalizes seamlessly to individual adversarial perturbations, where we observe similar strong performance gains. Finally, we introduce a principled procedure for learning feature constraints directly from data, enabling broad applicability across domains with structured input spaces.

cs.LG↗

arXiv2025

KITE: Kernelized and Information Theoretic Exemplars for In-Context Learning

In-context learning (ICL) has emerged as a powerful paradigm for adapting large language models (LLMs) to new and data-scarce tasks using only a few carefully selected task-specific examples presented in the prompt. However, given the limited context size of LLMs, a fundamental question arises: Which examples should be selected to maximize performance on a given user query? While nearest-neighbor-based methods like KATE have been widely adopted for this purpose, they suffer from well-known drawbacks in high-dimensional embedding spaces, including poor generalization and a lack of diversity. In this work, we study this problem of example selection in ICL from a principled, information theory-driven perspective. We first model an LLM as a linear function over input embeddings and frame the example selection task as a query-specific optimization problem: selecting a subset of exemplars from a larger example bank that minimizes the prediction error on a specific query. This formulation departs from traditional generalization-focused learning theoretic approaches by targeting accurate prediction for a specific query instance. We derive a principled surrogate objective that is approximately submodular, enabling the use of a greedy algorithm with an approximation guarantee. We further enhance our method by (i) incorporating the kernel trick to operate in high-dimensional feature spaces without explicit mappings, and (ii) introducing an optimal design-based regularizer to encourage diversity in the selected examples. Empirically, we demonstrate significant improvements over standard retrieval methods across a suite of classification tasks, highlighting the benefits of structure-aware, diverse example selection for ICL in real-world, label-scarce scenarios.

cs.LG↗

arXiv2025

DP-NCB: Privacy Preserving Fair Bandits

Multi-armed bandit algorithms are fundamental tools for sequential decision-making under uncertainty, with widespread applications across domains such as clinical trials and personalized decision-making. As bandit algorithms are increasingly deployed in these socially sensitive settings, it becomes critical to protect user data privacy and ensure fair treatment across decision rounds. While prior work has independently addressed privacy and fairness in bandit settings, the question of whether both objectives can be achieved simultaneously has remained largely open. Existing privacy-preserving bandit algorithms typically optimize average regret, a utilitarian measure, whereas fairness-aware approaches focus on minimizing Nash regret, which penalizes inequitable reward distributions, but often disregard privacy concerns. To bridge this gap, we introduce Differentially Private Nash Confidence Bound (DP-NCB)-a novel and unified algorithmic framework that simultaneously ensures $ε$-differential privacy and achieves order-optimal Nash regret, matching known lower bounds up to logarithmic factors. The framework is sufficiently general to operate under both global and local differential privacy models, and is anytime, requiring no prior knowledge of the time horizon. We support our theoretical guarantees with simulations on synthetic bandit instances, showing that DP-NCB incurs substantially lower Nash regret than state-of-the-art baselines. Our results offer a principled foundation for designing bandit algorithms that are both privacy-preserving and fair, making them suitable for high-stakes, socially impactful applications.

cs.LG↗

arXiv2025

Active Preference Optimization for Sample Efficient RLHF

Large Language Models (LLMs) aligned using Reinforcement Learning from Human Feedback (RLHF) have shown remarkable generation abilities in numerous tasks. However, collecting high-quality human preferences creates costly bottlenecks in practical deployments, and hence, training data are often budgeted. In these scenarios, it is crucial to collect training data (e.g., contexts, a pair of generations for each context, and a preference indicating which generation is better) carefully, yet most of the existing methods sample contexts uniformly at random from a given collection. Given this, under the Bradley-Terry-Luce preference model and with a small budget of training data, we show that uniform sampling of contexts could lead to a policy (i.e., an aligned model) that suffers a constant sub-optimality gap from the optimal policy. This highlights the need for an adaptive context sampling strategy for effective alignment under a small sample budget. To address this, we reformulate RLHF within the contextual preference bandit framework, treating generations as actions, and give a nearly complete characterization of the sub-optimality gap in terms of both lower and upper bounds. First, when the action set is a $d$-dimensional hypercube and the number of samples is $T$, we show an $Ω(d/\sqrt{T})$ lower bound. Next, we propose an algorithm, $\textit{Active Preference Optimization}$ ($\texttt{APO}$), that iteratively collects preferences for the most uncertain contexts. We show that the sub-optimality gap of the policy learned via $\texttt{APO}$ matches the lower bound up to a log factor and a non-linearity constant. Finally, we perform experiments on practical datasets to validate $\texttt{APO}$'s efficacy over existing methods, establishing it as a sample-efficient and cost-effective solution for LLM alignment.

cs.LG↗

arXiv2024

Provably Robust DPO: Aligning Language Models with Noisy Feedback

Learning from preference-based feedback has recently gained traction as a promising approach to align language models with human interests. While these aligned generative models have demonstrated impressive capabilities across various tasks, their dependence on high-quality human preference data poses a bottleneck in practical applications. Specifically, noisy (incorrect and ambiguous) preference pairs in the dataset might restrict the language models from capturing human intent accurately. While practitioners have recently proposed heuristics to mitigate the effect of noisy preferences, a complete theoretical understanding of their workings remain elusive. In this work, we aim to bridge this gap by by introducing a general framework for policy optimization in the presence of random preference flips. We focus on the direct preference optimization (DPO) algorithm in particular since it assumes that preferences adhere to the Bradley-Terry-Luce (BTL) model, raising concerns about the impact of noisy data on the learned policy. We design a novel loss function, which de-bias the effect of noise on average, making a policy trained by minimizing that loss robust to the noise. Under log-linear parameterization of the policy class and assuming good feature coverage of the SFT policy, we prove that the sub-optimality gap of the proposed robust DPO (rDPO) policy compared to the optimal policy is of the order $O(\frac{1}{1-2ε}\sqrt{\frac{d}{n}})$, where $ε< 1/2$ is flip rate of labels, $d$ is policy parameter dimension and $n$ is size of dataset. Our experiments on IMDb sentiment generation and Anthropic's helpful-harmless dataset show that rDPO is robust to noise in preference labels compared to vanilla DPO and other heuristics proposed by practitioners.

cs.LG↗

arXiv2023

GAR-meets-RAG Paradigm for Zero-Shot Information Retrieval

Given a query and a document corpus, the information retrieval (IR) task is to output a ranked list of relevant documents. Combining large language models (LLMs) with embedding-based retrieval models, recent work shows promising results on the zero-shot retrieval problem, i.e., no access to labeled data from the target domain. Two such popular paradigms are generation-augmented retrieval or GAR (generate additional context for the query and then retrieve), and retrieval-augmented generation or RAG (retrieve relevant documents as context and then generate answers). The success of these paradigms hinges on (i) high-recall retrieval models, which are difficult to obtain in the zero-shot setting, and (ii) high-precision (re-)ranking models which typically need a good initialization. In this work, we propose a novel GAR-meets-RAG recurrence formulation that overcomes the challenges of existing paradigms. Our method iteratively improves retrieval (via GAR) and rewrite (via RAG) stages in the zero-shot setting. A key design principle is that the rewrite-retrieval stages improve the recall of the system and a final re-ranking stage improves the precision. We conduct extensive experiments on zero-shot passage retrieval benchmarks, BEIR and TREC-DL. Our method establishes a new state-of-the-art in the BEIR benchmark, outperforming previous best results in Recall@100 and nDCG@10 metrics on 6 out of 8 datasets, with up to 17% relative gains over the previous best.

cs.CL↗

arXiv2023

Differentially Private Reward Estimation with Preference Feedback

Learning from preference-based feedback has recently gained considerable traction as a promising approach to align generative models with human interests. Instead of relying on numerical rewards, the generative models are trained using reinforcement learning with human feedback (RLHF). These approaches first solicit feedback from human labelers typically in the form of pairwise comparisons between two possible actions, then estimate a reward model using these comparisons, and finally employ a policy based on the estimated reward model. An adversarial attack in any step of the above pipeline might reveal private and sensitive information of human labelers. In this work, we adopt the notion of label differential privacy (DP) and focus on the problem of reward estimation from preference-based feedback while protecting privacy of each individual labelers. Specifically, we consider the parametric Bradley-Terry-Luce (BTL) model for such pairwise comparison feedback involving a latent reward parameter $θ^* \in \mathbb{R}^d$. Within a standard minimax estimation framework, we provide tight upper and lower bounds on the error in estimating $θ^*$ under both local and central models of DP. We show, for a given privacy budget $ε$ and number of samples $n$, that the additional cost to ensure label-DP under local model is $Θ\big(\frac{1}{ e^ε-1}\sqrt{\frac{d}{n}}\big)$, while it is $Θ\big(\frac{\text{poly}(d)}{εn} \big)$ under the weaker central model. We perform simulations on synthetic data that corroborate these theoretical results.

cs.LG↗

arXiv2023

Bregman Deviations of Generic Exponential Families

We revisit the method of mixture technique, also known as the Laplace method, to study the concentration phenomenon in generic exponential families. Combining the properties of Bregman divergence associated with log-partition function of the family with the method of mixtures for super-martingales, we establish a generic bound controlling the Bregman divergence between the parameter of the family and a finite sample estimate of the parameter. Our bound is time-uniform and makes appear a quantity extending the classical information gain to exponential families, which we call the Bregman information gain. For the practitioner, we instantiate this novel bound to several classical families, e.g., Gaussian, Bernoulli, Exponential, Weibull, Pareto, Poisson and Chi-square yielding explicit forms of the confidence sets and the Bregman information gain. We further numerically compare the resulting confidence bounds to state-of-the-art alternatives for time-uniform concentration and show that this novel method yields competitive results. Finally, we highlight the benefit of our concentration bounds on some illustrative applications.

cs.LG↗

arXiv2023

Differentially Private Episodic Reinforcement Learning with Heavy-tailed Rewards

In this paper, we study the problem of (finite horizon tabular) Markov decision processes (MDPs) with heavy-tailed rewards under the constraint of differential privacy (DP). Compared with the previous studies for private reinforcement learning that typically assume rewards are sampled from some bounded or sub-Gaussian distributions to ensure DP, we consider the setting where reward distributions have only finite $(1+v)$-th moments with some $v \in (0,1]$. By resorting to robust mean estimators for rewards, we first propose two frameworks for heavy-tailed MDPs, i.e., one is for value iteration and another is for policy optimization. Under each framework, we consider both joint differential privacy (JDP) and local differential privacy (LDP) models. Based on our frameworks, we provide regret upper bounds for both JDP and LDP cases and show that the moment of distribution and privacy budget both have significant impacts on regrets. Finally, we establish a lower bound of regret minimization for heavy-tailed MDPs in JDP model by reducing it to the instance-independent lower bound of heavy-tailed multi-armed bandits in DP model. We also show the lower bound for the problem in LDP by adopting some private minimax methods. Our results reveal that there are fundamental differences between the problem of private RL with sub-Gaussian and that with heavy-tailed rewards.

cs.LG↗

arXiv2023

On Differentially Private Federated Linear Contextual Bandits

We consider cross-silo federated linear contextual bandit (LCB) problem under differential privacy, where multiple silos (agents) interact with the local users and communicate via a central server to realize collaboration while without sacrificing each user's privacy. We identify three issues in the state-of-the-art: (i) failure of claimed privacy protection and (ii) incorrect regret bound due to noise miscalculation and (iii) ungrounded communication cost. To resolve these issues, we take a two-step principled approach. First, we design an algorithmic framework consisting of a generic federated LCB algorithm and flexible privacy protocols. Then, leveraging the proposed framework, we study federated LCBs under two different privacy constraints. We first establish privacy and regret guarantees under silo-level local differential privacy, which fix the issues present in state-of-the-art algorithm. To further improve the regret performance, we next consider shuffle model of differential privacy, under which we show that our algorithm can achieve nearly ``optimal'' regret without a trusted server. We accomplish this via two different schemes -- one relies on a new result on privacy amplification via shuffling for DP mechanisms and another one leverages the integration of a shuffle protocol for vector sum into the tree-based mechanism, both of which might be of independent interest. Finally, we support our theoretical results with numerical evaluations over contextual bandit instances generated from both synthetic and real-life data.

cs.LG↗

arXiv2023

Exploration in Linear Bandits with Rich Action Sets and its Implications for Inference

We present a non-asymptotic lower bound on the eigenspectrum of the design matrix generated by any linear bandit algorithm with sub-linear regret when the action set has well-behaved curvature. Specifically, we show that the minimum eigenvalue of the expected design matrix grows as $Ω(\sqrt{n})$ whenever the expected cumulative regret of the algorithm is $O(\sqrt{n})$, where $n$ is the learning horizon, and the action-space has a constant Hessian around the optimal arm. This shows that such action-spaces force a polynomial lower bound rather than a logarithmic lower bound, as shown by \cite{lattimore2017end}, in discrete (i.e., well-separated) action spaces. Furthermore, while the previous result is shown to hold only in the asymptotic regime (as $n \to \infty$), our result for these "locally rich" action spaces is any-time. Additionally, under a mild technical assumption, we obtain a similar lower bound on the minimum eigen value holding with high probability. We apply our result to two practical scenarios -- \emph{model selection} and \emph{clustering} in linear bandits. For model selection, we show that an epoch-based linear bandit algorithm adapts to the true model complexity at a rate exponential in the number of epochs, by virtue of our novel spectral bound. For clustering, we consider a multi agent framework where we show, by leveraging the spectral result, that no forced exploration is necessary -- the agents can run a linear bandit algorithm and estimate their underlying parameters at once, and hence incur a low regret.

cs.LG↗