arXiv subjects

Anupam Gupta

Publications and source records attributed to Anupam Gupta.

At least 37 records · Page 2Linked to original sources

arXiv2026

Combinatorial Optimization using Comparison Oracles

In linear combinatorial optimization, we aim to find $S^* = \arg\min_{S \in \mathcal{F}} \langle w,\mathbf{1}_S \rangle$ for a family $\mathcal{F} \subseteq 2^U$ over a ground set $U$ of $n$ elements. Traditionally, $w$ is known or accessible via a value oracle. Motivated by practical applications involving pairwise preferences, we study the weaker and more robust comparison oracle, which for any $S, T \in \mathcal{F}$ reveals only if $w(S) <, =, \text{ or } > w(T)$. We investigate the query complexity and computational efficiency of optimizing in this model. We present three main contributions. (1) Query Complexity: We establish that the query complexity over any arbitrary set system $\mathcal{F} \subseteq 2^U$ is $\tilde{O}(n^2)$. This demonstrates a fundamental separation between information and computational complexity, as the runtime may still be exponential for NP-hard problems. (2) Algorithmic Frameworks: We develop two general tools. First, a Dual Ellipsoid framework establishes an efficient reduction from optimization to certification. It shows that to optimize efficiently, it suffices to efficiently certify a candidate's optimality using only comparisons. Second, Global Subspace Learning (GSL) sorts all feasible sets using $O(nB \log(nB))$ queries for integer weights bounded by $B$. We efficiently implement GSL for linear matroids, yielding improved query complexities for problems like $k$-SUM, SUBSET-SUM, and $A+B$ sorting. (3) Combinatorial Applications: We give the first polynomial-time, low-query algorithms for classic problems, including minimum cuts, minimum weight spanning trees (and matroid bases), bipartite matching (and matroid intersection), and shortest $s$-$t$ paths. Our work provides the first general query complexity bounds and efficient algorithmic results for this fundamental model.

cs.DS↗

arXiv2026

Contextual Online Bilateral Trade

We study repeated bilateral trade when the valuations of the sellers and the buyers are contextual. More precisely, the agents' valuations are given by the inner product of a context vector with two unknown $d$-dimensional vectors -- one for the buyers and one for the sellers. At each time step $t$, the learner receives a context and posts two prices, one for the seller and one for the buyer, and the trade happens if both agents accept their price. We study two objectives for this problem, gain from trade and profit, proving no-regret with respect to a surprisingly strong benchmark: the best omniscient dynamic strategy. In the natural scenario where the learner observes \emph{separately} whether the agents accept their price -- the so-called \emph{two-bit} feedback -- we design algorithms that achieve $O(d\log d)$ regret for gain from trade, and $O(d \log\log T + d\log d)$ regret for profit maximization. Both results are tight, up to the $\log(d)$ factor, and implement per-step budget balance, meaning that the learner never incurs negative profit. In the less informative \emph{one-bit} feedback model, the learner only observes whether a trade happens or not. For this scenario, we show that the tight two-bit regret regimes are still attainable, at the cost of allowing the learner to possibly incur a small negative profit of order $O(d\log d)$, which is notably independent of the time horizon. As a final set of results, we investigate the combination of one-bit feedback and per-step budget balance. There, we design an algorithm for gain from trade that suffers regret independent of the time horizon, but \emph{exponential} in the dimension $d$. For profit maximization, we maintain this exponential dependence on the dimension, which gets multiplied by a $\log T$ factor.

cs.GT↗

arXiv2026

Learning Markov Decision Processes under Fully Bandit Feedback

A standard assumption in Reinforcement Learning is that the agent observes every visited state-action pair in the associated Markov Decision Process (MDP), along with the per-step rewards. Strong theoretical results are known in this setting, achieving nearly-tight $Θ(\sqrt{T})$-regret bounds. However, such detailed feedback can be unrealistic, and recent research has investigated more restricted settings such as trajectory feedback, where the agent observes all the visited state-action pairs, but only a single \emph{aggregate} reward. In this paper, we consider a far more restrictive ``fully bandit'' feedback model for episodic MDPs, where the agent does not even observe the visited state-action pairs -- it only learns the aggregate reward. We provide the first efficient bandit learning algorithm for episodic MDPs with $\widetilde{O}(\sqrt{T})$ regret. Our regret has an exponential dependence on the horizon length $\H$, which we show is necessary. We also obtain improved nearly-tight regret bounds for ``ordered'' MDPs; these can be used to model classical stochastic optimization problems such as $k$-item prophet inequality and sequential posted pricing. Finally, we evaluate the empirical performance of our algorithm for the setting of $k$-item prophet inequalities; despite the highly restricted feedback, our algorithm's performance is comparable to that of a state-of-art learning algorithm (UCB-VI) with detailed state-action feedback.

cs.LG↗

arXiv2025

Motility-Driven Viscoelastic Control of Tissue Morphology in Presomitic Mesoderm

Embryonic tissues deform across broad spatial and temporal scales and relax stress through active rearrangements. A quantitative link between cell-scale activity, spatial forcing, and emergent tissue-scale mechanics remains incomplete. Here, we use a vertex-based tissue model with active force fluctuations to study how motility controls viscoelastic response. After validation against experimental presomitic mesoderm relaxation dynamics, we extract intrinsic mechanical timescales using stress relaxation and oscillatory shear. The model captures motility-dependent shifts between elastic and viscous behavior and the coexistence of fast relaxation with long-lived residual stress. When subjected to spatially patterned, temporally pulsed forcing, tissues behave as mechanical filters: long-wavelength inputs are accumulated, whereas short-wavelength, cell-scale perturbations are rapidly erased, largely independent of motility. Simulations with localized motility hotspots, motivated by spatially confined FGF signaling reported in vertebrate limb development, produce sustained protrusive tissue deformations consistent with experimentally observed early bud-like morphologies. Together, these results establish a minimal framework linking motility-driven activity to wavelength-selective mechanical memory and emergent tissue patterning.

physics.bio-ph↗

arXiv2025

Complexity of Local Search for CSPs Parameterized by Constraint Difference

In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset $S$ of a universe $U$, the new input consists of a current solution $P$ (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution $S^*$, the goal is to find a feasible solution as good as $S^*$ in parameterized time $f(k) \cdot n^{O(1)}$, where $k$ denotes the distance $|PΔS^*|$. This model generalizes numerous classical parameterized optimization problems whose parameter $k$ is the minimum number of elements removed from $U$ to make it feasible, which corresponds to the case $P = U$. We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where $U$ is the set of constraints, and a subset $U'$ of constraints is feasible if there is an assignment to the variables satisfying all constraints in $U'$. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate's acceptance depends on the number of true literals.

cs.DS↗

arXiv2025

Steiner Forest: A Simplified Better-Than-2 Approximation

In the Steiner Forest problem, we are given a graph with edge lengths, and a collection of demand pairs; the goal is to find a subgraph of least total length such that each demand pair is connected in this subgraph. For over twenty years, the best approximation ratio known for the problem was a $2$-approximation due to Agrawal, Klein, and Ravi (STOC 1991), despite many attempts to surpass this bound. Finally, in a recent breakthrough, Ahmadi, Gholami, Hajiaghayi, Jabbarzade, and Mahdavi (FOCS 2025) gave a $2-\varepsilon$-approximation, where $\varepsilon \approx 10^{-11}$. In this work, we show how to simplify and extend the work of Ahmadi et al. to obtain an improved $1.994$-approximation. We combine some ideas from their work (e.g., an extended run of the moat-growing primal-dual algorithm, and identifying autarkic pairs) with other ideas -- submodular maximization to find components to contract, as in the relative greedy algorithms for Steiner tree, and the use of autarkic triples. We hope that our cleaner abstraction will open the way for further improvements.

cs.DS↗

arXiv2025

A Learning Perspective on Random-Order Covering Problems

In the random-order online set cover problem, the instance with $m$ sets and $n$ elements is chosen in a worst-case fashion, but then the elements arrive in a uniformly random order. Can this random-order model allow us to circumvent the bound of $O(\log m \log n)$-competitiveness for the adversarial arrival order model? This long-standing question was recently resolved by Gupta et al. (2021), who gave an algorithm that achieved an $O(\log mn)$-competitive ratio. While their LearnOrCover was inspired by ideas in online learning (and specifically the multiplicative weights update method), the analysis proceeded by showing progress from first principles. In this work, we show a concrete connection between random-order set cover and stochastic mirror-descent/online convex optimization. In particular, we show how additive/multiplicative regret bounds for the latter translate into competitiveness for the former. Indeed, we give a clean recipe for this translation, allowing us to extend our results to covering integer programs, set multicover, and non-metric facility location in the random order model, matching (and giving simpler proofs of) the previous applications of the LearnOrCover framework.

cs.DS↗

arXiv2025

Fully-Dynamic Submodular Cover with Bounded Recourse

In submodular covering problems, we are given a monotone, nonnegative submodular function $f: 2^N \rightarrow\mathbb{R}_+$ and wish to find the min-cost set $S\subseteq N$ such that $f(S)=f(N)$. This captures SetCover when $f$ is a coverage function. We introduce a general framework for solving such problems in a fully-dynamic setting where the function $f$ changes over time, and only a bounded number of updates to the solution (recourse) is allowed. For concreteness, suppose a nonnegative monotone submodular function $g_t$ is added or removed from an active set $G^{(t)}$ at each time $t$. If $f^{(t)}=\sum_{g\in G^{(t)}} g$ is the sum of all active functions, we wish to maintain a competitive solution to SubmodularCover for $f^{(t)}$ as this active set changes, and with low recourse. We give an algorithm that maintains an $O(\log(f_{max}/f_{min}))$-competitive solution, where $f_{max}, f_{min}$ are the largest/smallest marginals of $f^{(t)}$. The algorithm guarantees a total recourse of $O(\log(c_{max}/ c_{min})\cdot\sum_{t\leq T}g_t(N))$, where $c_{max},c_{min}$ are the largest/smallest costs of elements in $N$. This competitive ratio is best possible even in the offline setting, and the recourse bound is optimal up to the logarithmic factor. For monotone submodular functions that also have positive mixed third derivatives, we show an optimal recourse bound of $O(\sum_{t\leq T}g_t(N))$. This structured class includes set-coverage functions, so our algorithm matches the known $O(\log n)$-competitiveness and $O(1)$ recourse guarantees for fully-dynamic SetCover. Our work simultaneously simplifies and unifies previous results, as well as generalizes to a significantly larger class of covering problems. Our key technique is a new potential function inspired by Tsallis entropy. We also extensively use the idea of Mutual Coverage, which generalizes the classic notion of mutual information.

cs.DS↗

arXiv2025

The Online Submodular Cover Problem

In the submodular cover problem, we are given a monotone submodular function $f$, and we want to pick the min-cost set $S$ such that $f(S) = f(N)$. Motivated by problems in network monitoring and resource allocation, we consider the submodular cover problem in an online setting. As a concrete example, suppose at each time $t$, a nonnegative monotone submodular function $g_t$ is given to us. We define $f^{(t)} = \sum_{s \leq t} g_s$ as the sum of all functions seen so far. We need to maintain a submodular cover of these submodular functions $f^{(1)}, f^{(2)}, \ldots f^{(T)}$ in an online fashion; i.e., we cannot revoke previous choices. Formally, at each time $t$ we produce a set $S_t \subseteq N$ such that $f^{(t)}(S_t) = f^{(t)}(N)$ -- i.e., this set $S_t$ is a cover -- such that $S_{t-1} \subseteq S_t$, so previously decisions to pick elements cannot be revoked. (We actually allow more general sequences $\{f^{(t)}\}$ of submodular functions, but this sum-of-simpler-submodular-functions case is useful for concreteness.) We give polylogarithmic competitive algorithms for this online submodular cover problem. The competitive ratio on an input sequence of length $T$ is $O(\ln n \ln (T \cdot f(N) / f_{\text{min}}))$, where $f_{\text{min}}$ is the smallest nonzero marginal for functions $f^{(t)}$, and $|N| = n$. For the special case of online set cover, our competitive ratio matches that of Alon et al. [SIAM J. Comp. 03], which are best possible for polynomial-time online algorithms unless $NP \subseteq BPP$ (see Korman 04). Since existing offline algorithms for submodular cover are based on greedy approaches which seem difficult to implement online, the technical challenge is to (approximately) solve the exponential-sized linear programming relaxation for submodular cover, and to round it, both in the online setting.

cs.DS↗

arXiv2025

The Average-Value Allocation Problem

We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of $\frac{e}{e-1}$, and provide a $\frac{4e}{e-1}$-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.

cs.DS↗

arXiv2025

A Little Clairvoyance Is All You Need

We revisit the classical problem of minimizing the total flow time of jobs on a single machine in the online setting where jobs arrive over time. It has long been known that the Shortest Remaining Processing Time (SRPT) algorithm is optimal (i.e., $1$-competitive) when the job sizes are known up-front [Schrage, 1968]. But in the non-clairvoyant setting where job sizes are revealed only when the job finishes, no algorithm can be constant-competitive [Motwani, Phillips, and Torng, 1994]. We consider the $\varepsilon$-clairvoyant setting, where $\varepsilon \in [0,1]$, and each job's processing time becomes known once its remaining processing time equals an $\varepsilon$ fraction of its processing time. This captures settings where the system user uses the initial $(1-\varepsilon)$ fraction of a job's processing time to learn its true length, which it can then reveal to the algorithm. The model was proposed by Yingchareonthawornchai and Torng (2017), and it smoothly interpolates between the clairvoyant setting (when $ε= 1$) and the non-clairvoyant setting (when $\varepsilon = 0$). In a concrete sense, we are asking: how much knowledge is required to circumvent the hardness of this problem? We show that a little knowledge is enough, and that a constant competitive algorithm exists for every constant $\varepsilon > 0$. More precisely, for all $\varepsilon \in (0,1)$, we present a deterministic $\smash{\lceil \frac{1}{\varepsilon}\rceil}$-competitive algorithm, which is optimal for deterministic algorithms. We also present a matching lower bound (up to a constant factor) for randomized algorithms. Our algorithm to achieve this bound is remarkably simple and applies the ``optimism in the face of uncertainty'' principle. The proof relies on maintaining a matching between the jobs in the optimum's queue and the algorithm's queue, with small prefix expansion.

cs.DS↗

arXiv2025

Matroid-Based TSP Rounding for Half-Integral Solutions

We show how to round any half-integral solution to the subtour-elimination relaxation for the TSP, while losing a less-than-1.5 factor. Such a rounding algorithm was recently given by Karlin, Klein, and Oveis Gharan based on sampling from max-entropy distributions. We build on an approach of Haddadan and Newman to show how sampling from the matroid intersection polytope, and a new use of max-entropy sampling, can give better guarantees.

cs.DS↗

arXiv2025

Why is My Route Different Today? An Algorithm for Explaining Route Selection

Users of routing services like Apple Maps, Google Maps, and Waze frequently wonder why a given route is proposed. This question particularly arises when dynamic conditions like traffic and road closures cause unusual routes to be proposed. While many dynamic conditions may exist in a road network at any time, only a small fraction of those conditions are typically relevant to a given user's route. In this work, we introduce the concept of a simple valid explanation (SVE), which consists of a small set of traffic-laden road segments that answer the following question: Which traffic conditions cause a particular shortest traffic-aware route to differ from the shortest traffic-free route? We give an efficient algorithm for finding SVEs and show that they theoretically and experimentally lead to small and interpretable answers to the question.

cs.DS↗

arXiv2025

Effect of the background flow on the motility induced phase separation

We simulate active Brownian particles (ABPs) with soft-repulsive interactions subjected to a four-roll-mill flow. In the absence of flow, this system exhibits motility-induced phase separation (MIPS). To investigate the interplay between MIPS and flow-induced mixing, we introduce dimensionless parameters: a scaled time, $τ$, and a scaled velocity, ${\rm v}$, characterizing the ratio of ABP to fluid time and velocity scales, respectively. The parameter space defined by $τ$ and ${\rm v}$ reveals three distinct ABP distribution regimes. At low velocities ${\rm v} \ll 1$, flow dominates, leading to a homogeneous mixture. Conversely, at high velocities ${\rm v} \gg 1$, motility prevails, resulting in MIPS. In the intermediate regime (${\rm v} \sim 1$), the system's behavior depends on $τ$. For $τ<1$, a moderately mixed homogeneous phase emerges, while for $τ>1$, a novel phase, termed flow-induced phase separation (FIPS), arises due to the combined effects of flow topology and ABP motility and size. To characterize these phases, we analyze drift velocity, diffusivity, mean-squared displacement, giant number fluctuations, radial distribution function, and cluster-size distribution.

cond-mat.soft↗

arXiv2025

Onset of Intermittency and Multiscaling in Active Turbulence

Recent results suggest that highly active, chaotic, non-equilibrium states of living fluids might share much in common with high Reynolds number, inertial turbulence. We now show, by using a hydrodynamical model, the onset of intermittency and the consequent multiscaling of Eulerian and Lagrangian structure functions as a function of the bacterial activity. Our results bridge the worlds of low and high Reynolds number flows as well as open up intriguing possibilities of what makes flows intermittent.

cond-mat.soft↗

arXiv2025

Multi-Platform Autobidding with and without Predictions

We study the problem of finding the optimal bidding strategy for an advertiser in a multi-platform auction setting. The competition on a platform is captured by a value and a cost function, mapping bidding strategies to value and cost respectively. We assume a diminishing returns property, whereby the marginal cost is increasing in value. The advertiser uses an autobidder that selects a bidding strategy for each platform, aiming to maximize total value subject to budget and return-on-spend constraint. The advertiser has no prior information and learns about the value and cost functions by querying a platform with a specific bidding strategy. Our goal is to design algorithms that find the optimal bidding strategy with a small number of queries. We first present an algorithm that requires $O(m \log (mn) \log n)$ queries, where $m$ is the number of platforms and $n$ is the number of possible bidding strategies in each platform. Moreover, we adopt the learning-augmented framework and propose an algorithm that utilizes a (possibly erroneous) prediction of the optimal bidding strategy. We provide a $O(m \log (mη) \log η)$ query-complexity bound on our algorithm as a function of the prediction error $η$. This guarantee gracefully degrades to $O(m \log (mn) \log n)$. This achieves a ``best-of-both-worlds'' scenario: $O(m)$ queries when given a correct prediction, and $O(m \log (mn) \log n)$ even for an arbitrary incorrect prediction.

cs.GT↗

arXiv2024

Randomized Truthful Auctions with Learning Agents

We study a setting where agents use no-regret learning algorithms to participate in repeated auctions. \citet{kolumbus2022auctions} showed, rather surprisingly, that when bidders participate in second-price auctions using no-regret bidding algorithms, no matter how large the number of interactions $T$ is, the runner-up bidder may not converge to bidding truthfully. Our first result shows that this holds for \emph{general deterministic} truthful auctions. We also show that the ratio of the learning rates of the bidders can \emph{qualitatively} affect the convergence of the bidders. Next, we consider the problem of revenue maximization in this environment. In the setting with fully rational bidders, \citet{myerson1981optimal} showed that revenue can be maximized by using a second-price auction with reserves.We show that, in stark contrast, in our setting with learning bidders, \emph{randomized} auctions can have strictly better revenue guarantees than second-price auctions with reserves, when $T$ is large enough. Finally, we study revenue maximization in the non-asymptotic regime. We define a notion of {\em auctioneer regret} comparing the revenue generated to the revenue of a second price auction with truthful bids. When the auctioneer has to use the same auction throughout the interaction, we show an (almost) tight regret bound of $\smash{\widetilde Θ(T^{3/4})}.$ If the auctioneer can change auctions during the interaction, but in a way that is oblivious to the bids, we show an (almost) tight bound of $\smash{\widetilde Θ(\sqrt{T})}.$

cs.GT↗

arXiv2024

Position Coupling: Improving Length Generalization of Arithmetic Transformers Using Task Structure

Even for simple arithmetic tasks like integer addition, it is challenging for Transformers to generalize to longer sequences than those encountered during training. To tackle this problem, we propose position coupling, a simple yet effective method that directly embeds the structure of the tasks into the positional encoding of a (decoder-only) Transformer. Taking a departure from the vanilla absolute position mechanism assigning unique position IDs to each of the tokens, we assign the same position IDs to two or more "relevant" tokens; for integer addition tasks, we regard digits of the same significance as in the same position. On the empirical side, we show that with the proposed position coupling, our models trained on 1 to 30-digit additions can generalize up to 200-digit additions (6.67x of the trained length). On the theoretical side, we prove that a 1-layer Transformer with coupled positions can solve the addition task involving exponentially many digits, whereas any 1-layer Transformer without positional information cannot entirely solve it. We also demonstrate that position coupling can be applied to other algorithmic tasks such as Nx2 multiplication and a two-dimensional task.

cs.LG↗