arXiv subjects

Debabrota Basu

Publications and source records attributed to Debabrota Basu.

At least 19 recordsLinked to original sources

arXiv2026

Simulating Eutopia: Revisiting Long-term Fairness with Outcomes, Performativity, and Dynamics

As AI-driven Decision Makers (ADMs) influence our socioeconomic reality, their roles in both enhancing efficiency and amplifying the social biases have drawn attention. In this paper, we revisit the nuances of long-term `fairness' achievable by an ADM, specifically in the context of a credit lending induced wealth process. The literature on long-term fairness mostly (a) considers passive environments, i.e. the outcome of a predictor does not change the population's behaviour, and (b) measures bias in terms of disparity in instantaneous predictions rather than the downstream equity. These are not true for modern ADMs, like credit lenders. To address these caveats, we first formalise the wealth dynamics induced by a loan approving ADM interacting with a multi-demographic population as a performative Markov Decision Process with ADM level and social outcome level reward functions. Then, we mitigate the absence of such a performative test-bed by developing Eutopia: a lending-process simulator enabled with a novel performative data generator to learn long-term fair strategies. Finally, we test performative and classical RL algorithms with different fairness-aware and utilitarian utilities. Experimental results show that (a) learning with performative dynamics lead to better long-term efficiency and equity, and (b) learning with well-designed fairness-aware utility evaluated on social outcomes induces better efficiency, equity, and inclusivity.

cs.CY↗

arXiv2026

Bandits for Efficient Experimentation: Adapting to Control Group, Preferences, and Context Drifts

We consider a variant of the linear contextual stochastic multi-armed bandits, where the learner must provide recommendations to a group of users, each having its personalized preference vector, and in the presence of context distributions that are drifting over time. Under practitioner-friendly assumptions, we reduce this setting to linear bandit with stationary mean but heteroskedastic and non-stationary noise. We further study the case when the learner must ensure the mean reward of each decision must exceed that of a baseline strategy $\boldsymbol{\pi}_0$ at each decision step. We introduce Dri-MED, an algorithm inspired from the linear version of the MED strategy, and carefully adapted to handle the non-stationary heteroskedastic noise. We show that the instance-dependent regret scales as $\tilde{\mathcal O}\left(\frac{\kappa}{\tilde{\Delta}}d^2(\log(T)\right)$, where $\tilde{\Delta}$ is the constraint-aware sub-optimality gap subject to policy $\pi_0$, with variance-aware multiplicative term $\kappa$ that we carefully handle using heteroskedastic regression. We further show Dri-MED enjoys $\tilde{\mathcal{O}}(d)$ expected constraint violations. Our numerical results suggest that Dri-MED significantly outperforms conservative baselines that ignores the drift and preference structure.

cs.LG↗

arXiv2026

DOT: Dynamic Knob Selection and Online Sampling for Automated Database Tuning

Database Management Systems (DBMS) are crucial for efficient data management and access control, but their administration remains challenging for Database Administrators (DBAs). Tuning, in particular, is known to be difficult. Modern systems have many tuning parameters, but only a subset significantly impacts performance. Focusing on these influential parameters reduces the search space and optimizes performance. Current methods rely on costly warm-up phases and human expertise to identify important tuning parameters. In this paper, we present DOT, a dynamic knob selection and online sampling DBMS tuning algorithm. DOT uses Recursive Feature Elimination with Cross-Validation (RFECV) to prune low-importance tuning parameters and a Likelihood Ratio Test (LRT) strategy to balance exploration and exploitation. For parameter search, DOT uses a Bayesian Optimization (BO) algorithm to optimize configurations on-the-fly, eliminating the need for warm-up phases or prior knowledge (although existing knowledge can be incorporated). Experiments show that DOT achieves matching or outperforming performance compared to state-of-the-art tuners while substantially reducing tuning overhead.

cs.DB↗

arXiv2026

Asymptotically Optimal Sequential Testing with Markovian Data

We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic, finite-state Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the alternative corresponds to a disjoint set $Q$. We establish a non-asymptotic instance-dependent lower bound on the expected stopping time of any valid sequential test under the alternative, which is asymptotically tight. Our novel analysis improves the existing lower bounds, which are either asymptotic or provably sub-optimal in this setting. Our lower bound incorporates both the stationary distribution and the transition structure induced by the unknown Markov chain. We further propose an optimal test whose expected stopping time matches this lower bound asymptotically as $\alpha \to 0$. We illustrate the usefulness of our framework through applications to sequential detection of model misspecification in Markov Chain Monte Carlo and to testing structural properties, such as the linearity of transition dynamics, in Markov decision processes. Our findings yield a sharp and general characterization of optimal sequential testing procedures under Markovian dependence.

math.ST↗

arXiv2026

Sequential Membership Inference Attacks

Modern AI models are not static. They go through multiple updates in their lifecycles. We propose to design Sequential Membership Inference (SeMI) attacks leading to tighter privacy audits by exploiting the sequence of models and injecting a target canary at a controlled insertion time. First, for empirical mean computation, we develop SeMI*, an {optimal SeMI attack to identify the presence of a target inserted at a specific insertion step}. We derive the power of SeMI* to show that accessing the model sequence yields more powerful MI attacks than scrutinising only the final model. SeMI* exhibits an isolation property -- its power depends on the statistics obtained right before and after insertion of the target. Leveraging this insight, we develop practical white-box (accessing model gradients) and black-box (accessing loss) SeMI attacks against models trained with (DP-)SGD. Across datasets and models trained with (DP-)SGD, our experiments show that SeMI attacks achieve higher powers than snapshot-independent baselines, and yield tighter privacy audits thanks to (a) control over the insertion time and (b) observations across the model sequence.

cs.LG↗

arXiv2026

Auditing Fairness under Model Updates: Fundamental Complexity and Property-Preserving Updates

As machine learning models become increasingly embedded in societal infrastructure, auditing them for bias is of growing importance. However, in real-world deployments, auditing is complicated by the fact that model owners may adaptively update their models in response to changing environments, such as financial markets. These updates can alter the underlying model class while preserving certain properties of interest, raising fundamental questions about what can be reliably audited under such shifts. In this work, we study group fairness auditing under arbitrary updates. We consider general shifts that modify the pre-audit model class while maintaining invariance of the audited property. Our goals are two-fold: (i) to characterize the information complexity of allowable updates, by identifying which strategic changes preserve the property under audit; and (ii) to efficiently estimate auditing properties, such as group fairness, using a minimal number of labeled samples. We propose a generic framework for PAC auditing based on an Empirical Property Optimization (EPO) oracle. For statistical parity, we establish distribution-free auditing bounds characterized by the SP dimension, a novel combinatorial measure that captures the complexity of admissible strategic updates. Finally, we demonstrate that our framework naturally extends to other auditing objectives, including prediction error and robust risk.

cs.LG↗

arXiv2025

Performative Policy Gradient: Optimality in Performative Reinforcement Learning

Post-deployment machine learning algorithms often influence the environments they act in, and thus shift the underlying dynamics that the standard reinforcement learning (RL) methods ignore. While designing optimal algorithms in this performative setting has recently been studied in supervised learning, the RL counterpart remains under-explored. In this paper, we prove the performative counterparts of the performance difference lemma and the policy gradient theorem in RL, and further introduce the Performative Policy Gradient algorithm (PePG). PePG is the first policy gradient algorithm designed to account for performativity in RL. Under softmax parametrisation, and also with and without entropy regularisation, we prove that PePG converges to performatively optimal policies, i.e. policies that remain optimal under the distribution shifts induced by themselves. Thus, PePG significantly extends the prior works in Performative RL that achieves performative stability but not optimality. Furthermore, our empirical analysis on standard performative RL environments validate that PePG outperforms the existing performative RL algorithms aiming for stability.

cs.LG↗

arXiv2025

Test-time Verification via Optimal Transport: Coverage, ROC, & Sub-optimality

While test-time scaling with verification has shown promise in improving the performance of large language models (LLMs), the role of the verifier and its imperfections remain underexplored. The effect of verification manifests through interactions of three quantities: (i) the generator's coverage, (ii) the verifier's region of convergence (ROC), and (iii) the sampling algorithm's sub-optimality. Though recent studies capture subsets of these factors, a unified framework quantifying the geometry of their interplay is missing. We frame verifiable test-time scaling as a transport problem. This characterizes the interaction of coverage, ROC, and sub-optimality, and uncovers that the sub-optimality--coverage curve exhibits three regimes. A transport regime -- where sub-optimality increases with coverage, a policy improvement regime -- where sub-optimality may decrease with coverage, depending on the verifier's ROC, and a saturation regime -- where sub-optimality plateaus, unaffected by coverage. We further propose and analyze two classes of sampling algorithms -- sequential and batched, and examine how their computational complexities shape these trade-offs. Empirical results with Qwen, Llama, and Gemma models corroborate our theoretical findings.

cs.AI↗

arXiv2025

Dimension Agnostic Testing of Survey Data Credibility through the Lens of Regression

Assessing whether a sample survey credibly represents the population is a critical question for ensuring the validity of downstream research. Generally, this problem reduces to estimating the distance between two high-dimensional distributions, which typically requires a number of samples that grows exponentially with the dimension. However, depending on the model used for data analysis, the conclusions drawn from the data may remain consistent across different underlying distributions. In this context, we propose a task-based approach to assess the credibility of sampled surveys. Specifically, we introduce a model-specific distance metric to quantify this notion of credibility. We also design an algorithm to verify the credibility of survey data in the context of regression models. Notably, the sample complexity of our algorithm is independent of the data dimension. This efficiency stems from the fact that the algorithm focuses on verifying the credibility of the survey data rather than reconstructing the underlying regression model. Furthermore, we show that if one attempts to verify credibility by reconstructing the regression model, the sample complexity scales linearly with the dimensionality of the data. We prove the theoretical correctness of our algorithm and numerically demonstrate our algorithm's performance.

cs.LG↗

arXiv2025

FraPPE: Fast and Efficient Preference-based Pure Exploration

Preference-based Pure Exploration (PrePEx) aims to identify with a given confidence level the set of Pareto optimal arms in a vector-valued (aka multi-objective) bandit, where the reward vectors are ordered via a (given) preference cone $\mathcal{C}$. Though PrePEx and its variants are well-studied, there does not exist a computationally efficient algorithm that can optimally track the existing lower bound for arbitrary preference cones. We successfully fill this gap by efficiently solving the minimisation and maximisation problems in the lower bound. First, we derive three structural properties of the lower bound that yield a computationally tractable reduction of the minimisation problem. Then, we deploy a Frank-Wolfe optimiser to accelerate the maximisation problem in the lower bound. Together, these techniques solve the maxmin optimisation problem in $\mathcal{O}(KL^{2})$ time for a bandit instance with $K$ arms and $L$ dimensional reward, which is a significant acceleration over the literature. We further prove that our proposed PrePEx algorithm, FraPPE, asymptotically achieves the optimal sample complexity. Finally, we perform numerical experiments across synthetic and real datasets demonstrating that FraPPE achieves the lowest sample complexities to identify the exact Pareto set among the existing algorithms.

cs.LG↗

arXiv2025

DP-SPRT: Differentially Private Sequential Probability Ratio Tests

We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy constraints, addressing a significant gap in previous work. DP-SPRT relies on a private mechanism that processes a sequence of queries and stops after privately determining when the query results fall outside a predefined interval. This OutsideInterval mechanism improves upon naive composition of existing techniques like AboveThreshold, achieving a factor-of-2 privacy improvement and thus potentially benefiting other continual monitoring procedures. We prove generic upper bounds on the error and sample complexity of DP-SPRT that can accommodate various noise distributions based on the practitioner's privacy needs. We exemplify them in two settings: Laplace noise (pure Differential Privacy) and Gaussian noise (R\'enyi differential privacy). In the former setting, by providing a lower bound on the sample complexity of any $\varepsilon$-DP test with prescribed type I and type II errors, we show that DP-SPRT is near optimal when both errors are small and the two hypotheses are close. Moreover, we conduct an experimental study revealing its good practical performance.

stat.ML↗

arXiv2025

The Fair Game: Auditing & Debiasing AI Algorithms Over Time

An emerging field of AI, namely Fair Machine Learning (ML), aims to quantify different types of bias (also known as unfairness) exhibited in the predictions of ML algorithms, and to design new algorithms to mitigate them. Often, the definitions of bias used in the literature are observational, i.e. they use the input and output of a pre-trained algorithm to quantify a bias under concern. In reality,these definitions are often conflicting in nature and can only be deployed if either the ground truth is known or only in retrospect after deploying the algorithm. Thus,there is a gap between what we want Fair ML to achieve and what it does in a dynamic social environment. Hence, we propose an alternative dynamic mechanism,"Fair Game",to assure fairness in the predictions of an ML algorithm and to adapt its predictions as the society interacts with the algorithm over time. "Fair Game" puts together an Auditor and a Debiasing algorithm in a loop around an ML algorithm. The "Fair Game" puts these two components in a loop by leveraging Reinforcement Learning (RL). RL algorithms interact with an environment to take decisions, which yields new observations (also known as data/feedback) from the environment and in turn, adapts future decisions. RL is already used in algorithms with pre-fixed long-term fairness goals. "Fair Game" provides a unique framework where the fairness goals can be adapted over time by only modifying the auditor and the different biases it quantifies. Thus,"Fair Game" aims to simulate the evolution of ethical and legal frameworks in the society by creating an auditor which sends feedback to a debiasing algorithm deployed around an ML system. This allows us to develop a flexible and adaptive-over-time framework to build Fair ML systems pre- and post-deployment.

cs.AI↗

arXiv2025

Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning

Equilibrium Propagation (EP) is a learning algorithm for training Energy-based Models (EBMs) on static inputs which leverages the variational description of their fixed points. Extending EP to time-varying inputs is a challenging problem, as the variational description must apply to the entire system trajectory rather than just fixed points, and careful consideration of boundary conditions becomes essential. In this work, we present Generalized Lagrangian Equilibrium Propagation (GLEP), which extends the variational formulation of EP to time-varying inputs. We demonstrate that GLEP yields different learning algorithms depending on the boundary conditions of the system, many of which are impractical for implementation. We then show that Hamiltonian Echo Learning (HEL) -- which includes the recently proposed Recurrent HEL (RHEL) and the earlier known Hamiltonian Echo Backpropagation (HEB) algorithms -- can be derived as a special case of GLEP. Notably, HEL is the only instance of GLEP we found that inherits the properties that make EP a desirable alternative to backpropagation for hardware implementations: it operates in a "forward-only" manner (i.e. using the same system for both inference and learning), it scales efficiently (requiring only two or more passes through the system regardless of model size), and enables local learning.

cs.LG↗

arXiv2025

Optimal Regret of Bernoulli Bandits under Global Differential Privacy

As sequential learning algorithms are increasingly applied to real life, ensuring data privacy while maintaining their utilities emerges as a timely question. In this context, regret minimisation in stochastic bandits under $\epsilon$-global Differential Privacy (DP) has been widely studied. Unlike bandits without DP, there is a significant gap between the best-known regret lower and upper bound in this setting, though they "match" in order. Thus, we revisit the regret lower and upper bounds of $\epsilon$-global DP algorithms for Bernoulli bandits and improve both. First, we prove a tighter regret lower bound involving a novel information-theoretic quantity characterising the hardness of $\epsilon$-global DP in stochastic bandits. Our lower bound strictly improves on the existing ones across all $\epsilon$ values. Then, we choose two asymptotically optimal bandit algorithms, i.e. DP-KLUCB and DP-IMED, and propose their DP versions using a unified blueprint, i.e., (a) running in arm-dependent phases, and (b) adding Laplace noise to achieve privacy. For Bernoulli bandits, we analyse the regrets of these algorithms and show that their regrets asymptotically match our lower bound up to a constant arbitrary close to 1. This refutes the conjecture that forgetting past rewards is necessary to design optimal bandit algorithms under global DP. At the core of our algorithms lies a new concentration inequality for sums of Bernoulli variables under Laplace mechanism, which is a new DP version of the Chernoff bound. This result is universally useful as the DP literature commonly treats the concentrations of Laplace noise and random variables separately, while we couple them to yield a tighter bound.

stat.ML↗

arXiv2025

Sublinear Algorithms for Wasserstein and Total Variation Distances: Applications to Fairness and Privacy Auditing

Resource-efficiently computing representations of probability distributions and the distances between them while only having access to the samples is a fundamental and useful problem across mathematical sciences. In this paper, we propose a generic framework to learn the probability and cumulative distribution functions (PDFs and CDFs) of a sub-Weibull, i.e. almost any light- or heavy-tailed, distribution while the samples from it arrive in a stream. The idea is to reduce these problems into estimating the frequency of an \textit{appropriately chosen subset} of the support of a \textit{properly discretised distribution}. We leverage this reduction to compute mergeable summaries of distributions from the stream of samples while requiring only sublinear space relative to the number of observed samples. This allows us to estimate Wasserstein and Total Variation (TV) distances between any two distributions while samples arrive in streams and from multiple sources. Our algorithms significantly improves on the existing methods for distance estimation incurring super-linear time and linear space complexities, and further extend the mergeable summaries framework to continuous distributions with possibly infinite support. Our results are tight with respect to the existing lower bounds for bounded discrete distributions. In addition, we leverage our proposed estimators of Wasserstein and TV distances to tightly audit the fairness and privacy of algorithms. We empirically demonstrate the efficiency of proposed algorithms across synthetic and real-world datasets.

cs.LG↗

arXiv2024

Isoperimetry is All We Need: Langevin Posterior Sampling for RL with Sublinear Regret

Common assumptions, like linear or RKHS models, and Gaussian or log-concave posteriors over the models, do not explain practical success of RL across a wider range of distributions and models. Thus, we study how to design RL algorithms with sublinear regret for isoperimetric distributions, specifically the ones satisfying the Log-Sobolev Inequality (LSI). LSI distributions include the standard setups of RL theory, and others, such as many non-log-concave and perturbed distributions. First, we show that the Posterior Sampling-based RL (PSRL) algorithm yields sublinear regret if the data distributions satisfy LSI and some mild additional assumptions. Also, when we cannot compute or sample from an exact posterior, we propose a Langevin sampling-based algorithm design: LaPSRL. We show that LaPSRL achieves order-optimal regret and subquadratic complexity per episode. Finally, we deploy LaPSRL with a Langevin sampler -- SARAH-LD, and test it for different bandit and MDP environments. Experimental results validate the generality of LaPSRL across environments and its competitive performance with respect to the baselines.

cs.LG↗

arXiv2024

Preference-based Pure Exploration

We study the preference-based pure exploration problem for bandits with vector-valued rewards. The rewards are ordered using a (given) preference cone $\mathcal{C}$ and our goal is to identify the set of Pareto optimal arms. First, to quantify the impact of preferences, we derive a novel lower bound on sample complexity for identifying the most preferred policy with a confidence level $1-\delta$. Our lower bound elicits the role played by the geometry of the preference cone and punctuates the difference in hardness compared to existing best-arm identification variants of the problem. We further explicate this geometry when the rewards follow Gaussian distributions. We then provide a convex relaxation of the lower bound and leverage it to design the Preference-based Track and Stop (PreTS) algorithm that identifies the most preferred policy. Finally, we show that the sample complexity of PreTS is asymptotically tight by deriving a new concentration inequality for vector-valued rewards.

stat.ML↗

arXiv2024

Dynamical-VAE-based Hindsight to Learn the Causal Dynamics of Factored-POMDPs

Learning representations of underlying environmental dynamics from partial observations is a critical challenge in machine learning. In the context of Partially Observable Markov Decision Processes (POMDPs), state representations are often inferred from the history of past observations and actions. We demonstrate that incorporating future information is essential to accurately capture causal dynamics and enhance state representations. To address this, we introduce a Dynamical Variational Auto-Encoder (DVAE) designed to learn causal Markovian dynamics from offline trajectories in a POMDP. Our method employs an extended hindsight framework that integrates past, current, and multi-step future information within a factored-POMDP setting. Empirical results reveal that this approach uncovers the causal graph governing hidden state transitions more effectively than history-based and typical hindsight-based models.

cs.LG↗