arXiv subjects

Haricharan Balasundaram

Publications and source records attributed to Haricharan Balasundaram.

8 recordsLinked to original sources

arXiv2026

Learning to Transmit Over Unknown Erasure Channels with Empirical Erasure Rate Feedback

We address the problem of reliable data transmission within a finite time horizon $T$ over a binary erasure channel with unknown erasure probability. We consider a feedback model wherein the transmitter can query the receiver infrequently and obtain the empirical erasure rate experienced by the latter. We aim to minimize a regret quantity, i.e. how much worse a strategy performs compared to an oracle who knows the probability of erasure, while operating at the same block error rate. A learning vs. exploitation dilemma manifests in this scenario -- specifically, we need to balance between (i) learning the erasure probability with reasonable accuracy and (ii) utilizing the channel to transmit as many information bits as possible. We propose two strategies: (i) a two-phase approach using rate estimation followed by transmission that achieves an $O({T}^{\frac 23})$ regret using only one query, and (ii) a windowing strategy using geometrically-increasing window sizes that achieves an $O({\sqrt{T}})$ regret using $O(\log(T))$ queries.

cs.IT↗

arXiv2026

Convex Optimization with Nested Evolving Feasible Sets

\emph{Convex Optimization with Nested Evolving Feasible Sets (CONES)} is considered where the objective function $f$ remains fixed but the feasible region evolves over time as a nested sequence $S_1 \supseteq S_2 \supseteq \cdots \supseteq S_T$. The goal of an online algorithm is to simultaneously minimize the regret with respect to hindsight static optimal benchmark and the total movement cost $M_\cA(T)$ while ensuring feasibility at all times. CONES is an optimization-oriented generalization of the well-known \emph{nested convex body chasing} (NCBC). When the loss function is convex, we propose a lazy-algorithm and show that it achieves $O(T^{1-β}), O(T^β)$ simultaneous regret and movement cost for any $β\in (0,1]$, over a time horizon of $T$. When the loss function is strongly convex, we propose a \textsc{Frugal} algorithm that simultaneously achieves zero regret and a movement cost of $O(\log T)$. To complement this, we show that any online algorithm with $o(T)$ regret has a movement cost of $Ω\left(\sqrt{\frac{\log{T}}{\log \log T}}\right)$.

cs.LG↗

arXiv2026

Stability Notions for Hospital Residents with Sizes

The Hospital Residents problem with sizes (HRS) is a generalisation of the well-studied hospital residents (HR) problem. In the HRS problem, an agent a has a size s(a) and the agent occupies s(a) many positions of the hospital h when assigned to h. The notion of stability in this setting is suitably modified, and it is known that deciding whether an HRS instance admits a stable matching is NP-hard under severe restrictions. In this work, we explore a variation of stability, which we term occupancy-based stability. This notion was defined by McDermid and Manlove (J. of Comb. Opt. 2010) but remained unexplored to the best of our knowledge. In our work, we show that every HRS instance admits an occupancy-stable matching. We further show that computing a maximum-size occupancy-stable matching is NP-hard, even in the presence of master list ordering. We complement our hardness result by providing an approximation algorithm with a guarantee strictly better than 3 for the max-size occupancy-stable matching problem. Given that the classical notion of stability adapted for HRS is not guaranteed to exist in general, we show a practical restriction under which a stable matching is guaranteed to exist. We present an efficient algorithm to output a stable matching in the restricted HRS instances. We also provide an alternate NP-hardness proof for the decision version of the stable matching problem for HRS which imposes a severe restriction on the number of neighbours of non-unit sized agents.

cs.DS↗

arXiv2026

Lower Bound on the Cumulative Constrained Violation for the OGD+Projection algorithm for Constrained Online Convex Optimization (COCO)

The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action $x_t \in \mathcal{X} \subset \mathbb{R}^d$, a convex loss function $f_t$ and a convex constraint function $g_t$ that drives the constraint $g_t(x)\le 0$ are revealed. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV) compared to the benchmark that knows the loss functions and constraint functions $f_t$ and $g_t$ for all $t$ ahead of time, and chooses a static optimal action that is feasible with respect to all $g_t(x)\le 0$. Currently, the best known algorithm is OGD+Projection algorithm of [Vaze and Sinha, 2025] that has simultaneous regret of $O(\sqrt{T})$ and CCV of $O(T^{1/3})$ for $d=2$ [Balasundaram et al., 2026], and simultaneous regret of $O(\sqrt{T})$ and CCV of $O(\sqrt{T})$ for any $d$ [Sarkar and Sinha, 2026]. In this paper, we show that the CCV of the OGD+Projection algorithm is $Ω(T^{\frac{d-1}{2d}})$. This is the first such lower bound result.

cs.LG↗

arXiv2026

Semantic Smoothing for Language Models via Distribution Estimation and Embeddings

We propose semantic smoothing, a smoothing method for language models that uses embeddings to share statistical observations across semantically similar contexts. The starting point is a decomposition of log-perplexity that motivates smoothing as a collection of distribution-estimation problems under Kullback-Leibler (KL) loss. We then show that, under a Lipschitz-logit model for embedding-based language generation, proximity of context embeddings implies proximity of the corresponding next-word distributions in KL divergence. Combining these observations, we formulate semantic smoothing as distribution estimation in KL loss with KL-proximity side information. For $n$ samples on a $d$-symbol alphabet with a side-information distribution at KL distance $Δ$, we give an interpolation estimator with worst-case KL risk $O(\min\{Δ,d/n\})$, and prove a matching-order lower bound for uniform side information. We extend the estimator to multiple and empirically estimated synonymous distributions. Experiments on synthetic Markov data and WikiText-103 bigram models using Word2Vec, GloVe, and GPT-2 embeddings show that semantic smoothing consistently reduces test perplexity when applied to add-constant and Kneser-Ney estimates.

cs.IT↗

arXiv2026

Breaking the $O(\sqrt{T})$ Cumulative Constraint Violation Barrier while Achieving $O(\sqrt{T})$ Static Regret in Constrained Online Convex Optimization

The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action $x_t \in \mathcal{X} \subset \mathbb{R}^d$, a convex loss function $f_t$ and a convex constraint function $g_t$ that drives the constraint $g_t(x)\le 0$ are revealed. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV) compared to the benchmark that knows the loss functions and constraint functions $f_t$ and $g_t$ for all $t$ ahead of time, and chooses a static optimal action that is feasible with respect to all $g_t(x)\le 0$. In recent prior work Sinha and Vaze [2024], algorithms with simultaneous regret of $O(\sqrt{T})$ and CCV of $O(\sqrt{T})$ or (CCV of $O(1)$ in specific cases Vaze and Sinha [2025], e.g. when $d=1$) have been proposed. It is widely believed that CCV is $Ω(\sqrt{T})$ for all algorithms that ensure that regret is $O(\sqrt{T})$ with the worst case input for any $d\ge 2$. In this paper, we refute this and show that the algorithm of Vaze and Sinha [2025] simultaneously achieves regret of $O(\sqrt{T})$ regret and CCV of $O(T^{1/3})$ when $d=2$.

cs.LG↗

arXiv2026

Distribution Estimation with Side Information

We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side information arises naturally through word semantics/similarities that can be inferred by closeness of vector word embeddings, for instance. We consider two specific models for side information--a local model where the unknown distribution is in the neighborhood of a known distribution, and a partial ordering model where the alphabet is partitioned into known higher and lower probability sets. In both models, we theoretically characterize the improvement in a suitable squared-error risk because of the available side information. Simulations over natural language and synthetic data illustrate these gains.

cs.IT↗

arXiv2025

Generalized Capacity Planning for the Hospital-Residents Problem

The Hospital Residents setting models important problems like school choice, assignment of undergraduate students to degree programs, among many others. In this setting, fixed quotas are associated with the programs that limit the number of agents that can be assigned to them. Motivated by scenarios where all agents must be matched, we propose and study a generalized capacity planning problem, which allows cost-controlled flexibility with respect to quotas. Our setting is an extension of the Hospital Resident setting where programs have the usual quota as well as an associated cost, indicating the cost of matching an agent beyond the initial quotas. We seek to compute a matching that matches all agents and is optimal with respect to preferences, and minimizes either a local or a global objective on cost. We show that there is a sharp contrast -- minimizing the local objective is polynomial-time solvable, whereas minimizing the global objective is NP-hard. On the positive side, we present approximation algorithms for the global objective in the general case and a particular hard case. We achieve the approximation guarantee for the special hard case via a linear programming based algorithm. We strengthen the NP-hardness by showing a matching lower bound to our algorithmic result.

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