arXiv subjects

Abhishek Sinha

Publications and source records attributed to Abhishek Sinha.

At least 19 recordsLinked to original sources

arXiv2026

A Geometric Approach to Constrained Online Learning

We study constrained online convex optimization with adversarial time-varying constraints. At each round the learner acts before observing the loss and constraint, and is compared with the best fixed action satisfying all constraints in hindsight. The goal is to obtain minimax-optimal regret while controlling cumulative constraint violation (CCV). Prior algorithms achieved $O(\log T)$ regret with $O(\sqrt{T\log T})$ CCV for strongly convex losses, and $O(\sqrt{T})$ regret with $O(\sqrt{T}\log T)$ CCV for convex losses. We present NP-OGD, an iterated nested-projection algorithm. For strongly convex losses it achieves $O(\log T)$ regret and $O(\log T)$ CCV; for convex losses it achieves $O(\sqrt{T})$ regret and $O(\sqrt{T})$ CCV. The analysis relies on a geometric movement bound: after lifting the nested projected-gradient trajectory to one higher dimension, the lifted path is self-contracted under a nonstandard norm, so a finite-length theorem for self-contracted curves controls the total projection movement. We also prove complementary lower bounds using layered sphere packings. For strongly convex losses, any online algorithm with polynomially sublinear regret can incur CCV at least $Ω((\log T)^{(d-1)/(d+1)}/\log\log T)$. For convex losses, we prove CCV lower bounds $Ω(T^{(d-1)/(2(d+3))})$ for weakly adaptive algorithms and $Ω(T^{(d-1)/(2d)})$ for NP-OGD. Finally, for the constrained experts special case over $N$ experts, an active Hedge algorithm attains $O(\sqrt{T\log N})$ regret and $O(N)$ CCV, with a matching minimax CCV lower bound for sufficiently large horizons.

cs.LG↗

arXiv2026

Constrained Contextual Bandits with Adversarial Contexts

We study budget-constrained contextual bandits with adversarial contexts, where each action yields a random reward and incurs a random cost. We adopt the standard realizability assumption: conditioned on the observed context, rewards and costs are drawn independently from fixed distributions whose expectations belong to known function classes. We focus on the continuing setting, in which the algorithm operates over the entire horizon even after the budget for cumulative cost is exhausted. In this setting, the objective is to simultaneously control regret and the violation of the budget constraint. Building on the seminal $\mathsf{SquareCB}$ framework of Foster et al. [2018], we propose a simple and modular framework that leverages online regression oracles to reduce the constrained problem to a standard unconstrained contextual bandit problem with adaptively defined surrogate reward functions. In contrast to prior works, which focus on stochastic contexts, our reduction yields improved guarantees for more general adversarial contexts, together with an efficient algorithm with a compact and transparent analysis.

cs.LG↗

arXiv2026

Projection-free Algorithms for Online Convex Optimization with Adversarial Constraints

We study a generalization of the Online Convex Optimization (OCO) framework with time-varying adversarial constraints. In this setting, at each round, the learner selects an action from a convex decision set $X$, after which both a convex cost function and a convex constraint function are revealed. The objective is to design a computationally efficient learning policy that simultaneously achieves low regret with respect to the cost functions and low cumulative constraint violation (CCV) over a horizon of length $T$. A major computational bottleneck in standard OCO algorithms is the projection operation onto the decision set $X$. However, for many structured decision sets, linear optimization can be performed efficiently. Motivated by this, we propose a projection-free online conditional gradient (OCG)-based algorithm that requires only a single call to a linear optimization oracle over $X$ per round. Our approach improves upon the state of the art for projection-free online learning with adversarial constraints, achieving $\tilde{O}(T^{\frac{3}{4}})$ bounds for both regret and CCV. Our algorithm is conceptually simple. It constructs a surrogate cost function as a nonnegative linear combination of the cost and constraint functions, and feeds these surrogate costs into a novel adaptive online conditional gradient subroutine introduced in this paper. We further extend our framework to the bandit setting, where we show that a new form of surrogate loss is necessary to properly handle bandit feedback - an issue overlooked in prior work. Finally, we develop an efficient Follow-the-Perturbed-Leader (FTPL)-based algorithm, particularly well-suited for online combinatorial optimization problems with discrete actions, which also achieves $O(T^{\frac{3}{4}})$ regret and CCV.

cs.LG↗

arXiv2026

A Simple Reduction Scheme for Constrained Contextual Bandits with Adversarial Contexts via Regression

We study constrained contextual bandits (CCB) with adversarially chosen contexts, where each action yields a random reward and incurs a random cost. We adopt the standard realizability assumption: conditioned on the observed context, rewards and costs are drawn independently from fixed distributions whose expectations belong to known function classes. We consider the continuing setting, in which the algorithm operates over the entire horizon even after the budget is exhausted. In this setting, the objective is to simultaneously control regret and cumulative constraint violation. Building on the seminal SquareCB framework of Foster et al. (2018), we propose a simple and modular algorithmic scheme that leverages online regression oracles to reduce the constrained problem to a standard unconstrained contextual bandit problem with adaptively defined surrogate reward functions. In contrast to most prior work on CCB, which focuses on stochastic contexts, our reduction yields improved guarantees for the more general adversarial context setting, together with a compact and transparent analysis.

cs.LG↗

arXiv2026

Universal Dynamic Regret and Constraint Violation Bounds for Constrained Online Convex Optimization

We consider a generalization of the celebrated Online Convex Optimization (OCO) framework with adversarial online constraints. In this problem, an online learner interacts with an adversary sequentially over multiple rounds. At the beginning of each round, the learner chooses an action from a convex decision set. After that, the adversary reveals a convex cost function and a convex constraint function. The goal of the learner is to minimize the cumulative cost while satisfying the constraints as tightly as possible. We present two efficient algorithms with simple modular structures that give universal dynamic regret and cumulative constraint violation bounds, improving upon state-of-the-art results. While the first algorithm, which achieves the optimal regret bound, involves projection onto the constraint sets, the second algorithm is projection-free and achieves better violation bounds in rapidly varying environments. Our results hold in the most general case when both the cost and constraint functions are chosen arbitrarily, and the constraint functions need not contain any fixed common feasible point. We establish these results by introducing a general framework that reduces the constrained learning problem to an instance of the standard OCO problem with specially constructed surrogate cost functions.

cs.LG↗

arXiv2025

Beyond $\tilde{O}(\sqrt{T})$ Constraint Violation for Online Convex Optimization with Adversarial Constraints

We study Online Convex Optimization with adversarial constraints (COCO). At each round a learner selects an action from a convex decision set and then an adversary reveals a convex cost and a convex constraint function. The goal of the learner is to select a sequence of actions to minimize both regret and the cumulative constraint violation (CCV) over a horizon of length $T$. The best-known policy for this problem achieves $O(\sqrt{T})$ regret and $\tilde{O}(\sqrt{T})$ CCV. In this paper, we improve this by trading off regret to achieve substantially smaller CCV. This trade-off is especially important in safety-critical applications, where satisfying the safety constraints is non-negotiable. Specifically, for any bounded convex cost and constraint functions, we propose an online policy that achieves $\tilde{O}(\sqrt{dT}+ T^β)$ regret and $\tilde{O}(dT^{1-β})$ CCV, where $d$ is the dimension of the decision set and $β\in [0,1]$ is a tunable parameter. We begin with a special case, called the $\textsf{Constrained Expert}$ problem, where the decision set is a probability simplex and the cost and constraint functions are linear. Leveraging a new adaptive small-loss regret bound, we propose a computationally efficient policy for the $\textsf{Constrained Expert}$ problem, that attains $O(\sqrt{T\ln N}+T^β)$ regret and $\tilde{O}(T^{1-β} \ln N)$ CCV for $N$ number of experts. The original problem is then reduced to the $\textsf{Constrained Expert}$ problem via a covering argument. Finally, with an additional $M$-smoothness assumption, we propose a computationally efficient first-order policy attaining $O(\sqrt{MT}+T^β)$ regret and $\tilde{O}(MT^{1-β})$ CCV.

cs.LG↗

arXiv2025

Optimal Anytime Algorithms for Online Convex Optimization with Adversarial Constraints

We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called \emph{anytime} if it provides a non-trivial performance guarantee for any intermediate timestep $t$ without requiring prior knowledge of the length of the entire time horizon $T$. Our proposed algorithm achieves optimal performance bounds without resorting to the standard doubling trick, which has poor practical performance due to multiple restarts. Our core technical contribution is the use of time-varying Lyapunov functions to keep track of constraint violations. This must be contrasted with prior works that used a fixed Lyapunov function tuned to the known horizon length $T$. The use of time-varying Lyapunov function poses unique analytical challenges as properties, such as \emph{monotonicity}, on which the prior proofs rest, no longer hold. By introducing a new analytical technique, we show that our algorithm achieves $O(\sqrt{t})$ regret and $\tilde{O}(\sqrt{t})$ cumulative constraint violation bounds for any $t\geq 1$. We extend our results to the dynamic regret setting, achieving bounds that adapt to the path length of the comparator sequence without prior knowledge of its total length. We also present an adaptive algorithm in the optimistic setting, whose performance gracefully scales with the cumulative prediction error. We demonstrate the practical utility of our algorithm through numerical experiments involving the online shortest path problem.

cs.LG↗

arXiv2025

Online Learning for Approximately-Convex Functions with Long-term Adversarial Constraints

We study an online learning problem with long-term budget constraints in the adversarial setting. In this problem, at each round $t$, the learner selects an action from a convex decision set, after which the adversary reveals a cost function $f_t$ and a resource consumption function $g_t$. The cost and consumption functions are assumed to be $α$-approximately convex - a broad class that generalizes convexity and encompasses many common non-convex optimization problems, including DR-submodular maximization, Online Vertex Cover, and Regularized Phase Retrieval. The goal is to design an online algorithm that minimizes cumulative cost over a horizon of length $T$ while approximately satisfying a long-term budget constraint of $B_T$. We propose an efficient first-order online algorithm that guarantees $O(\sqrt{T})$ $α$-regret against the optimal fixed feasible benchmark while consuming at most $O(B_T \log T)+ \tilde{O}(\sqrt{T})$ resources in both full-information and bandit feedback settings. In the bandit feedback setting, our approach yields an efficient solution for the $\texttt{Adversarial Bandits with Knapsacks}$ problem with improved guarantees. We also prove matching lower bounds, demonstrating the tightness of our results. Finally, we characterize the class of $α$-approximately convex functions and show that our results apply to a broad family of problems.

cs.LG↗

arXiv2025

Online Bidding Algorithms with Strict Return on Spend (ROS) Constraint

Auto-bidding problem under a strict return-on-spend constraint (ROSC) is considered, where an algorithm has to make decisions about how much to bid for an ad slot depending on the revealed value, and the hidden allocation and payment function that describes the probability of winning the ad-slot depending on its bid. The objective of an algorithm is to maximize the expected utility (product of ad value and probability of winning the ad slot) summed across all time slots subject to the total expected payment being less than the total expected utility, called the ROSC. A (surprising) impossibility result is derived that shows that no online algorithm can achieve a sub-linear regret even when the value, allocation and payment function are drawn i.i.d. from an unknown distribution. The problem is non-trivial even when the revealed value remains constant across time slots, and an algorithm with regret guarantee that is optimal up to logarithmic factor is derived.

cs.GT↗

arXiv2025

$O(\sqrt{T})$ Static Regret and Instance Dependent Constraint Violation for Constrained Online Convex Optimization

The constrained version of the standard online convex optimization (OCO) framework, called COCO is considered, where on every round, a convex cost function and a convex constraint function are revealed to the learner after it chooses the action for that round. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV). An algorithm is proposed that guarantees a static regret of $O(\sqrt{T})$ and a CCV of $\min\{\cV, O(\sqrt{T}\log T) \}$, where $\cV$ depends on the distance between the consecutively revealed constraint sets, the shape of constraint sets, dimension of action space and the diameter of the action space. For special cases of constraint sets, $\cV=O(1)$. Compared to the state of the art results, static regret of $O(\sqrt{T})$ and CCV of $O(\sqrt{T}\log T)$, that were universal, the new result on CCV is instance dependent, which is derived by exploiting the geometric properties of the constraint sets.

cs.LG↗

arXiv2025

Minimizing Queue Length Regret for Arbitrarily Varying Channels

We consider an online channel scheduling problem for a single transmitter-receiver pair equipped with $N$ arbitrarily varying wireless channels. The transmission rates of the channels might be non-stationary and could be controlled by an oblivious adversary. At every slot, incoming data arrives at an infinite-capacity data queue located at the transmitter. A scheduler, which is oblivious to the current channel rates, selects one of the $N$ channels for transmission. At the end of the slot, the scheduler only gets to know the transmission rate of the selected channel. The objective is to minimize the queue length regret, defined as the difference between the queue length at some time $T$ achieved by an online policy and the queue length obtained by always transmitting over the single best channel in hindsight. We propose a weakly adaptive Multi-Armed Bandit (MAB) algorithm for minimizing the queue length regret in this setup. Unlike previous works, we do not make any stability assumptions about the queue or the arrival process. Hence, our result holds even when the queueing process is unstable. Our main observation is that the queue length regret can be upper bounded by the regret of a MAB policy that competes against the best channel in hindsight uniformly over all sub-intervals of $[T]$. As a technical contribution of independent interest, we then propose a weakly adaptive adversarial MAB policy which achieves $\tilde{O}(\sqrt{N}T^{\frac{3}{4}})$ regret with high probability, implying the same bound for queue length regret.

cs.IT↗

arXiv2024

Optimal Algorithms for Online Convex Optimization with Adversarial Constraints

A well-studied generalization of the standard online convex optimization (OCO) framework is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the learner after it chooses the action for that round. The objective is to design an online learning policy that simultaneously achieves a small regret while ensuring a small cumulative constraint violation (CCV) against an adaptive adversary interacting over a horizon of length $T$. A long-standing open question in COCO is whether an online policy can simultaneously achieve $O(\sqrt{T})$ regret and $\tilde{O}(\sqrt{T})$ CCV without any restrictive assumptions. For the first time, we answer this in the affirmative and show that a simple first-order policy can simultaneously achieve these bounds. Furthermore, in the case of strongly convex cost and convex constraint functions, the regret guarantee can be improved to $O(\log T)$ while keeping the CCV bound the same as above. We establish these results by effectively combining adaptive OCO policies as a blackbox with Lyapunov optimization - a classic tool from control theory. Surprisingly, the analysis is short and elegant.

cs.LG↗

arXiv2024

Confidence Is All You Need for MI Attacks

In this evolving era of machine learning security, membership inference attacks have emerged as a potent threat to the confidentiality of sensitive data. In this attack, adversaries aim to determine whether a particular point was used during the training of a target model. This paper proposes a new method to gauge a data point's membership in a model's training set. Instead of correlating loss with membership, as is traditionally done, we have leveraged the fact that training examples generally exhibit higher confidence values when classified into their actual class. During training, the model is essentially being 'fit' to the training data and might face particular difficulties in generalization to unseen data. This asymmetry leads to the model achieving higher confidence on the training data as it exploits the specific patterns and noise present in the training data. Our proposed approach leverages the confidence values generated by the machine learning model. These confidence values provide a probabilistic measure of the model's certainty in its predictions and can further be used to infer the membership of a given data point. Additionally, we also introduce another variant of our method that allows us to carry out this attack without knowing the ground truth(true class) of a given data point, thus offering an edge over existing label-dependent attack methods.

cs.LG↗

arXiv2024

Tight Bounds for Online Convex Optimization with Adversarial Constraints

A well-studied generalization of the standard online convex optimization (OCO) is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the learner after the action for that round is chosen. The objective is to design an online policy that simultaneously achieves a small regret while ensuring small cumulative constraint violation (CCV) against an adaptive adversary. A long-standing open question in COCO is whether an online policy can simultaneously achieve $O(\sqrt{T})$ regret and $O(\sqrt{T})$ CCV without any restrictive assumptions. For the first time, we answer this in the affirmative and show that an online policy can simultaneously achieve $O(\sqrt{T})$ regret and $\tilde{O}(\sqrt{T})$ CCV. We establish this result by effectively combining the adaptive regret bound of the AdaGrad algorithm with Lyapunov optimization - a classic tool from control theory. Surprisingly, the analysis is short and elegant.

cs.LG↗

arXiv2024

BanditQ: Fair Bandits with Guaranteed Rewards

Classic no-regret multi-armed bandit algorithms, including the Upper Confidence Bound (UCB), Hedge, and EXP3, are inherently unfair by design. Their unfairness stems from their objective of playing the most rewarding arm as frequently as possible while ignoring the rest. In this paper, we consider a fair prediction problem in the stochastic setting with a guaranteed minimum rate of accrual of rewards for each arm. We study the problem in both full-information and bandit feedback settings. Combining queueing-theoretic techniques with adversarial bandits, we propose a new online policy, called BanditQ, that achieves the target reward rates while conceding a regret and target rate violation penalty of at most $O(T^{\frac{3}{4}}).$ The regret bound in the full-information setting can be further improved to $O(\sqrt{T})$ under either a monotonicity assumption or when considering time-averaged regret. The proposed policy is efficient and admits a black-box reduction from the fair prediction problem to the standard adversarial MAB problem. The analysis of the BanditQ policy involves a new self-bounding inequality, which might be of independent interest.

cs.LG↗

arXiv2024

Zero-shot Active Learning Using Self Supervised Learning

Deep learning algorithms are often said to be data hungry. The performance of such algorithms generally improve as more and more annotated data is fed into the model. While collecting unlabelled data is easier (as they can be scraped easily from the internet), annotating them is a tedious and expensive task. Given a fixed budget available for data annotation, Active Learning helps selecting the best subset of data for annotation, such that the deep learning model when trained over that subset will have maximum generalization performance under this budget. In this work, we aim to propose a new Active Learning approach which is model agnostic as well as one doesn't require an iterative process. We aim to leverage self-supervised learnt features for the task of Active Learning. The benefit of self-supervised learning, is that one can get useful feature representation of the input data, without having any annotation.

cs.LG↗

arXiv2023

$α$-Fair Contextual Bandits

Contextual bandit algorithms are at the core of many applications, including recommender systems, clinical trials, and optimal portfolio selection. One of the most popular problems studied in the contextual bandit literature is to maximize the sum of the rewards in each round by ensuring a sublinear regret against the best-fixed context-dependent policy. However, in many applications, the cumulative reward is not the right objective - the bandit algorithm must be fair in order to avoid the echo-chamber effect and comply with the regulatory requirements. In this paper, we consider the $α$-Fair Contextual Bandits problem, where the objective is to maximize the global $α$-fair utility function - a non-decreasing concave function of the cumulative rewards in the adversarial setting. The problem is challenging due to the non-separability of the objective across rounds. We design an efficient algorithm that guarantees an approximately sublinear regret in the full-information and bandit feedback settings.

cs.LG↗

arXiv2023

No-regret Algorithms for Fair Resource Allocation

We consider a fair resource allocation problem in the no-regret setting against an unrestricted adversary. The objective is to allocate resources equitably among several agents in an online fashion so that the difference of the aggregate $α$-fair utilities of the agents between an optimal static clairvoyant allocation and that of the online policy grows sub-linearly with time. The problem is challenging due to the non-additive nature of the $α$-fairness function. Previously, it was shown that no online policy can exist for this problem with a sublinear standard regret. In this paper, we propose an efficient online resource allocation policy, called Online Proportional Fair (OPF), that achieves $c_α$-approximate sublinear regret with the approximation factor $c_α=(1-α)^{-(1-α)}\leq 1.445,$ for $0\leq α< 1$. The upper bound to the $c_α$-regret for this problem exhibits a surprising phase transition phenomenon. The regret bound changes from a power-law to a constant at the critical exponent $α=\frac{1}{2}.$ As a corollary, our result also resolves an open problem raised by Even-Dar et al. [2009] on designing an efficient no-regret policy for the online job scheduling problem in certain parameter regimes. The proof of our results introduces new algorithmic and analytical techniques, including greedy estimation of the future gradients for non-additive global reward functions and bootstrapping adaptive regret bounds, which may be of independent interest.

cs.LG↗