arXiv subjects

Udvas Das

Publications and source records attributed to Udvas Das.

7 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↗

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

Witness Set in Monotone Polygons: Exact and Approximate

Given a simple polygon $\mathscr{P}$, two points $x$ and $y$ within $\mathscr{P}$ are {\em visible} to each other if the line segment between $x$ and $y$ is contained in $\mathscr{P}$. The {\em visibility region} of a point $x$ includes all points in $\mathscr{P}$ that are visible from $x$. A point set $Q$ within a polygon $\mathscr{P}$ is said to be a \emph{witness set} for $\mathscr{P}$ if each point in $\mathscr{P}$ is visible from at most one point from $Q$. The problem of finding the largest size witness set in a given polygon was introduced by Amit et al. [Int. J. Comput. Geom. Appl. 2010]. Recently, Daescu et al. [Comput. Geom. 2019] gave a linear-time algorithm for this problem on monotone mountains. In this study, we contribute to this field by obtaining the largest witness set within both continuous and discrete models. In the {\sc Witness Set (WS)} problem, the input is a polygon $\mathscr{P}$, and the goal is to find a maximum-sized witness set in $\mathscr{P}$. In the {\sc Discrete Witness Set (DisWS)} problem, one is given a finite set of points $S$ alongside $\mathscr{P}$, and the task is to find a witness set $Q \subseteq S$ that maximizes $|Q|$. We investigate {\sc DisWS} in simple polygons, but consider {\sc WS} specifically for monotone polygons. Our main contribution is as follows: (1) a polynomial time algorithm for {\sc DisWS} for general polygons and (2) the discretization of the {\sc WS} problem for monotone polygons. Specifically, given a monotone polygon with $r$ reflex vertices, and a positive integer $k$ we generate a point set $Q$ with size $r^{O(k)} \cdot n$ such that $Q$ contains an witness set of size $k$ (if exists). This leads to an exact algorithm for {\sc WS} problem in monotone polygons running in time $r^{O(k)} \cdot n^{O(1)}$. We also provide a PTAS for this with running time $r^{O(1/\epsilon)} n^2$.

cs.CG↗

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

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↗

arXiv2024

Learning to Explore with Lagrangians for Bandits under Unknown Linear Constraints

Pure exploration in bandits formalises multiple real-world problems, such as tuning hyper-parameters or conducting user studies to test a set of items, where different safety, resource, and fairness constraints on the decision space naturally appear. We study these problems as pure exploration in multi-armed bandits with unknown linear constraints, where the aim is to identify an $r$-optimal and feasible policy as fast as possible with a given level of confidence. First, we propose a Lagrangian relaxation of the sample complexity lower bound for pure exploration under constraints. Second, we leverage properties of convex optimisation in the Lagrangian lower bound to propose two computationally efficient extensions of Track-and-Stop and Gamified Explorer, namely LATS and LAGEX. Then, we propose a constraint-adaptive stopping rule, and while tracking the lower bound, use optimistic estimate of the feasible set at each step. We show that LAGEX achieves asymptotically optimal sample complexity upper bound, while LATS shows asymptotic optimality up to novel constraint-dependent constants. Finally, we conduct numerical experiments with different reward distributions and constraints that validate efficient performance of LATS and LAGEX.

cs.LG↗