arXiv subjects

Mengxiao Zhang

Publications and source records attributed to Mengxiao Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Toward Optimal Switching Regret for Multi-Armed Bandits with Oblivious Adversary

We study switching regret in adversarial multi-armed bandits, where the learner competes with an arm sequence that changes at most $S$ times. When $S$ is known, an optimal expected regret of $\widetilde{\mathcal{O}}(\sqrt{(S+1)KT})$ is obtainable [Auer et al., 2002]. However, when $S$ is unknown, Marinov and Zimmert [2021] show that this guarantee is impossible under an adaptive adversary. In this paper, we show that a single algorithm achieves $\widetilde{\mathcal{O}}(\sqrt{(S+1)KT})$ expected regret for every $S$ against an oblivious adversary, resolving an open problem of Auer et al. [2019b]. Our algorithm combines a fixed-share learner initialized with a small learning rate and dyadic-interval subroutines that search for local improvements using randomized learning rates and implicit exploration. Importantly, a non-uniform prior favors following the main learner, keeping the cost of maintaining many subroutines small. When the subroutines accumulate sufficient improvement over the main learner, its learning rate doubles, allowing adaptation to the unknown number of comparator switches $S$.

cs.LG↗

arXiv2026

Minimax Alternating Regret for the Experts Problem and Online Convex Optimization

In this paper, we study alternating regret in online convex optimization (OCO), motivated by the success of alternating learning dynamics in two-player games. Although previous works have shown that $o(\sqrt{T})$ alternating regret is achievable under various assumptions on the loss functions and feasible domains, the minimax regret rate has remained open even for the expert problem. In this paper, we resolve this question by showing matching lower and upper bounds for both the expert problem and general OCO. Somewhat surprisingly, for the $d$-expert problem, we show that the minimax alternating regret is $Θ(\log d)$, independent of the horizon $T$. This significantly improves upon the best-known $\mathcal{O}(T^{1/3}\log^{2/3} d)$ established by Hait et al. [2025]. We further extend our results to general OCO over a $d$-dimensional compact convex set and prove that the worst-case minimax alternating regret is $Θ\left(d\log \left(1+\frac{T}{d}\right)\right)$, also significantly improving upon the best-known $\mathcal{O}((d\log T)^{2/3}T^{1/3})$ upper bound and resolving the open problem posed by Cevher et al. [2023], Hait et al. [2025]. Technically, our upper bound for the expert problem is achieved by a corrected variant of Hedge, in which carefully designed correction terms cancel the unfavorable curvature arising in the alternating-regret analysis. We extend the same corrected-potential argument to continuous action sets to obtain the optimal alternating-regret rate for OCO. For the lower bounds, the expert construction repeatedly eliminates half of the candidate experts, while the OCO lower bound instance construction replaces this discrete elimination by a more involved multiscale construction on the unit disk.

stat.ML↗

arXiv2026

Toward Optimal Second-Order Path-Length Guarantee for Adversarial Multi-Armed Bandits

We study second-order path-length regret in adversarial $K$-armed bandits against oblivious loss sequences. Bubeck et al. [2019] designed an algorithm that achieves $\widetilde{\mathcal{O}}(K+\sqrt{KQ_{\infty,1}})$ regret, where $Q_{\infty,1}$ is the first-order path length, and left open whether $\widetilde{\mathcal{O}}(\text{poly}(K)\sqrt{1+Q_{\infty,2}})$ regret is achievable under bandit feedback, where $Q_{\infty,2}$ is the second-order path length. Somewhat surprisingly, we resolve this question positively by showing that with a more involved analysis, the exact same algorithm of Bubeck et al. [2019] achieves $\mathcal{O}\left(K\log(KT)+\sqrt{K\log(KT)\bigl(1+Q_{\infty,2}\bigr)}\right)$ expected regret when $Q_{\infty,2}$ is known, where $T$ is the horizon. This matches the $Ω(\sqrt{KQ_{\infty,2}})$ lower bound up to logarithmic factors and additive terms. We further remove the knowledge of $Q_{\infty,2}$ using an adaptive restart scheme whose path-length estimator has uniformly bounded increments.

cs.LG↗

arXiv2026

Parameter-free Dynamic Regret: Time-varying Movement Costs, Delayed Feedback, and Memory

In this paper, we study dynamic regret in unconstrained online convex optimization (OCO) with movement costs. Specifically, we generalize the standard setting by allowing the movement cost coefficients $λ_t$ to vary arbitrarily over time. Our main contribution is a novel algorithm that establishes the first comparator-adaptive dynamic regret bound for this setting, guaranteeing $\widetilde{\mathcal{O}}(\sqrt{(M^2+MP_T)(T+\sum_t λ_t)})$ regret, where $P_T$ is the path length of the comparator sequence over $T$ rounds and $M$ is the maximal comparator norm. Our result recovers the optimal adaptive rates for both static and dynamic regret in OCO as the special case where $λ_t=0$ for all rounds. To demonstrate the versatility of our results, we consider two applications: OCO with delayed feedback and OCO with time-varying memory. We show that both problems can be translated into time-varying movement costs, establishing a novel reduction specifically for the delayed feedback setting that is of independent interest. A crucial observation is that the first-order dependence on movement costs in our regret bound plays a key role in enabling optimal comparator-adaptive dynamic regret guarantees in both settings.

cs.LG↗

arXiv2026

Near-Optimal Regret for Distributed Adversarial Bandits: A Black-Box Approach

We study distributed adversarial bandits, where $N$ agents cooperate to minimize the global average loss while observing only their own local losses. We show that the minimax regret for this problem is $\tildeΘ(\sqrt{(ρ^{-1/2}+K/N)T})$, where $T$ is the horizon, $K$ is the number of actions, and $ρ$ is the spectral gap of the communication matrix. Our algorithm, based on a novel black-box reduction to bandits with delayed feedback, requires agents to communicate only through gossip. It achieves an upper bound that significantly improves over the previous best bound $\tilde{O}(ρ^{-1/3}(KT)^{2/3})$ of Yi and Vojnovic (2023). We complement this result with a matching lower bound, showing that the problem's difficulty decomposes into a communication cost $ρ^{-1/4}\sqrt{T}$ and a bandit cost $\sqrt{KT/N}$. We further demonstrate the versatility of our approach by deriving first-order and best-of-both-worlds bounds in the distributed adversarial setting. Finally, we extend our framework to distributed linear bandits in $R^d$, obtaining a regret bound of $\tilde{O}(\sqrt{(ρ^{-1/2}+1/N)dT})$, achieved with only $O(d)$ communication cost per agent and per round via a volumetric spanner.

cs.LG↗

arXiv2026

Near-Optimal Stochastic Linear Bandits with Delay

We study stochastic linear bandits with delayed feedback under several delay models and establish near-optimal regret guarantees. Our results identify when delayed linear bandits exhibit the same qualitative behavior as multi-armed bandits (MAB), and when the linear structure creates fundamentally new challenges. Specifically, (1) for \emph{loss-independent delays}, where the delay does not depend on the realized loss (but potentially depends on the arm), we show that delays incur only an additive regret penalty. Under stochastic delays, this penalty scales with the expected delay, while under adversarial delays, it scales with the maximum number of outstanding observations. Notably, both delay penalties are dimension-free, improving upon the state-of-the-art results; (2) for \emph{loss-dependent delays}, we show that linear bandits are substantially harder than MAB: unlike in MAB, we prove matching (up to log factors) upper and lower bounds in linear bandits, whose delay penalty depends on the square root of the dimension. (3) for the \emph{delay-as-payoff model}, a special case of loss-dependent delay, we show that the optimal MAB guarantee, which depends only on the delay of the optimal arm, is also unattainable in linear bandits. Together, these results provide a sharp characterization of how delayed feedback interacts with linear generalization.

cs.LG↗

arXiv2026

Near-Optimal Last-Iterate Convergence for Zero-Sum Games with Bandit Feedback and Opponent Actions

Last-iterate convergence of learning dynamics in games has attracted significant recent attention. In two-player zero-sum games with bandit feedback, where only the loss of the selected action pair is observed, Fiegel et al. (2025) show a separation between average-iterate and last-iterate convergence in duality gap: while the optimal t^(-1/2) rate after t rounds is achievable for the former via standard no-regret algorithms, the latter cannot converge faster than t^(-1/3) in expectation or t^(-1/4) with high probability. However, in many practical settings, such as preference learning, the players observe not only their loss but also the opponent's action. This raises a natural question: can such additional information enable faster last-iterate convergence? We answer this question affirmatively, showing that t^(-1/2) last-iterate convergence is achievable with high probability in this setting, via an efficient algorithm that updates its strategy infrequently by solving an estimated log-barrier-regularized game. We identify fundamental obstacles preventing standard analysis for multi-armed bandits, the single-player case, from generalizing to games, and develop a novel analysis to overcome them. Experiments confirm that our algorithm indeed converges faster than naive baselines and prior methods that do not exploit opponent-action feedback. Finally, we note that our results also improve those for dueling bandits, a special case with skew-symmetric game matrices.

cs.LG↗

arXiv2026

An LP-Based Approach for Bilinear Saddle Point Problem with Instance-dependent Guarantee and Noisy Feedback

In this work, we study the sample complexity of obtaining a Nash equilibrium (NE) estimate in two-player zero-sum matrix games with noisy feedback. Specifically, we propose a novel algorithm that repeatedly solves linear programs (LPs) to obtain an NE estimate with bias at most $\varepsilon$ with a sample complexity of $O\left(\frac{m_1 m_2}{\varepsilon\min\{δ^2,σ_0^2,σ^3\}} \log\frac{m_1 m_2}{\varepsilon}\right)$ for general $m_1 \times m_2$ game matrices, where $σ$, $σ_0$, $δ$ are some problem-dependent constants. To our knowledge, this is the first instance-dependent sample complexity bound for finding an NE estimate with $\varepsilon$ bias in general-dimension matrix games with noisy feedback and potentially non-unique equilibria. Our algorithm builds on recent advances in online resource allocation and operates in two stages: (1) identifying the support set of an NE, and (2) computing the unique NE restricted to this support. Both stages rely on a careful analysis of LP solutions derived from noisy samples.

math.OC↗

arXiv2026

Pricing Query Complexity of Multiplicative Revenue Approximation

We study the pricing query complexity of revenue maximization for a single buyer whose private valuation is drawn from an unknown distribution. In this setting, the seller must learn the optimal monopoly price by posting prices and observing only binary purchase decisions, rather than the realized valuations. Prior work has established tight query complexity bounds for learning a near-optimal price with additive error $\varepsilon$ when the valuation distribution is supported on $[0,1]$. However, our understanding of how to learn a near-optimal price that achieves at least a $(1-\varepsilon)$ fraction of the optimal revenue remains limited. In this paper, we study the pricing query complexity of the single-buyer revenue maximization problem under such multiplicative error guarantees in several settings. Observe that when pricing queries are the only source of information about the buyer's distribution, no algorithm can achieve a non-trivial approximation, since the scale of the distribution cannot be learned from pricing queries alone. Motivated by this fundamental impossibility, we consider two natural and well-motivated models that provide "scale hints": (i) a one-sample hint, in which the algorithm observes a single realized valuation before making pricing queries; and (ii) a value-range hint, in which the valuation support is known to lie within $[1, H]$. For each type of hint, we establish pricing query complexity guarantees that are tight up to polylogarithmic factors for several classes of distributions, including monotone hazard rate (MHR) distributions, regular distributions, and general distributions.

cs.GT↗

arXiv2026

Interaction-Grounded Learning for Contextual Markov Decision Processes with Personalized Feedback

In this paper, we study Interaction-Grounded Learning (IGL) [Xie et al., 2021], a paradigm designed for realistic scenarios where the learner receives indirect feedback generated by an unknown mechanism, rather than explicit numerical rewards. While prior work on IGL provides efficient algorithms with provable guarantees, those results are confined to single-step settings, restricting their applicability to modern sequential decision-making systems such as multi-turn Large Language Model (LLM) deployments. To bridge this gap, we propose a computationally efficient algorithm that achieves a sublinear regret guarantee for contextual episodic Markov Decision Processes (MDPs) with personalized feedback. Technically, we extend the reward-estimator construction of Zhang et al. [2024a] from the single-step to the multi-step setting, addressing the unique challenges of decoding latent rewards under MDPs. Building on this estimator, we design an Inverse-Gap-Weighting (IGW) algorithm for policy optimization. Finally, we demonstrate the effectiveness of our method in learning personalized objectives from multi-turn interactions through experiments on both a synthetic episodic MDP and a real-world user booking dataset.

cs.LG↗

arXiv2026

Decentralized Online Convex Optimization with Unknown Feedback Delays

Decentralized online convex optimization (D-OCO), where multiple agents within a network collaboratively learn optimal decisions in real-time, arises naturally in applications such as federated learning, sensor networks, and multi-agent control. In this paper, we study D-OCO under unknown, time-and agent-varying feedback delays. While recent work has addressed this problem (Nguyen et al., 2024), existing algorithms assume prior knowledge of the total delay over agents and still suffer from suboptimal dependence on both the delay and network parameters. To overcome these limitations, we propose a novel algorithm that achieves an improved regret bound of O N $\sqrt$ d tot + N $\sqrt$ T (1-$σ$2) 1/4 , where T is the total horizon, d tot denotes the average total delay across agents, N is the number of agents, and 1 -$σ$ 2 is the spectral gap of the network. Our approach builds upon recent advances in D-OCO (Wan et al., 2024a), but crucially incorporates an adaptive learning rate mechanism via a decentralized communication protocol. This enables each agent to estimate delays locally using a gossip-based strategy without the prior knowledge of the total delay. We further extend our framework to the strongly convex setting and derive a sharper regret bound of O N $δ$max ln T $α$ , where $α$ is the strong convexity parameter and $δ$ max is the maximum number of missing observations averaged over agents. We also show that our upper bounds for both settings are tight up to logarithmic factors. Experimental results validate the effectiveness of our approach, showing improvements over existing benchmark algorithms.

stat.ML↗

arXiv2025

Comparator-Adaptive $Φ$-Regret: Improved Bounds, Simpler Algorithms, and Applications to Games

In the classic expert problem, $Φ$-regret measures the gap between the learner's total loss and that achieved by applying the best action transformation $ϕ\in Φ$. A recent work by Lu et al., [2025] introduces an adaptive algorithm whose regret against a comparator $ϕ$ depends on a certain sparsity-based complexity measure of $ϕ$, (almost) recovering and interpolating optimal bounds for standard regret notions such as external, internal, and swap regret. In this work, we propose a general idea to achieve an even better comparator-adaptive $Φ$-regret bound via much simpler algorithms compared to Lu et al., [2025]. Specifically, we discover a prior distribution over all possible binary transformations and show that it suffices to achieve prior-dependent regret against these transformations. Then, we propose two concrete and efficient algorithms to achieve so, where the first one learns over multiple copies of a prior-aware variant of the Kernelized MWU algorithm of Farina et al., [2022], and the second one learns over multiple copies of a prior-aware variant of the BM-reduction [Blum and Mansour, 2007]. To further showcase the power of our methods and the advantages over Lu et al., [2025] besides the simplicity and better regret bounds, we also show that our second approach can be extended to the game setting to achieve accelerated and adaptive convergence rate to $Φ$-equilibria for a class of general-sum games. When specified to the special case of correlated equilibria, our bound improves over the existing ones from Anagnostides et al., [2022a,b]

cs.LG↗

arXiv2025

Defective Convolutional Networks

Robustness of convolutional neural networks (CNNs) has gained in importance on account of adversarial examples, i.e., inputs added as well-designed perturbations that are imperceptible to humans but can cause the model to predict incorrectly. Recent research suggests that the noises in adversarial examples break the textural structure, which eventually leads to wrong predictions. To mitigate the threat of such adversarial attacks, we propose defective convolutional networks that make predictions relying less on textural information but more on shape information by properly integrating defective convolutional layers into standard CNNs. The defective convolutional layers contain defective neurons whose activations are set to be a constant function. As defective neurons contain no information and are far different from standard neurons in its spatial neighborhood, the textural features cannot be accurately extracted, and so the model has to seek other features for classification, such as the shape. We show extensive evidence to justify our proposal and demonstrate that defective CNNs can defense against black-box attacks better than standard CNNs. In particular, they achieve state-of-the-art performance against transfer-based attacks without any adversarial training being applied.

cs.CV↗

arXiv2025

Alternating Regret for Online Convex Optimization

Motivated by alternating learning dynamics in two-player games, a recent work by Cevher et al.(2024) shows that $o(\sqrt{T})$ alternating regret is possible for any $T$-round adversarial Online Linear Optimization (OLO) problem, and left as an open question whether the same is true for general Online Convex Optimization (OCO). We answer this question in the affirmative by showing that the continuous Hedge algorithm achieves $\tilde{\mathcal{O}}(d^{\frac{2}{3}}T^{\frac{1}{3}})$ alternating regret for any adversarial $d$-dimensional OCO problems. We show that this implies an alternating learning dynamic that finds a Nash equilibrium for any convex-concave zero-sum games or a coarse correlated equilibrium for any convex two-player general-sum games at a rate of $\tilde{\mathcal{O}}(d^{\frac{2}{3}}/T^{\frac{2}{3}})$. To further improve the time complexity and/or the dimension dependence, we propose another simple algorithm, Follow-the-Regularized-Leader with a regularizer whose convex conjugate is 3rd-order smooth, for OCO with smooth and self-concordant loss functions (such as linear or quadratic losses). We instantiate our algorithm with different regularizers and show that, for example, when the decision set is the $\ell_2$ ball, our algorithm achieves $\tilde{\mathcal{O}}(T^{\frac{2}{5}})$ alternating regret with no dimension dependence (and a better $\tilde{\mathcal{O}}(T^{\frac{1}{3}})$ bound for quadratic losses). We complement our results by showing some algorithm-specific alternating regret lower bounds, including a somewhat surprising $Ω(\sqrt{T})$ lower bound for a Regret Matching variant that is widely used in alternating learning dynamics.

cs.LG↗

arXiv2025

Exploiting Curvature in Online Convex Optimization with Delayed Feedback

In this work, we study the online convex optimization problem with curved losses and delayed feedback. When losses are strongly convex, existing approaches obtain regret bounds of order $d_{\max} \ln T$, where $d_{\max}$ is the maximum delay and $T$ is the time horizon. However, in many cases, this guarantee can be much worse than $\sqrt{d_{\mathrm{tot}}}$ as obtained by a delayed version of online gradient descent, where $d_{\mathrm{tot}}$ is the total delay. We bridge this gap by proposing a variant of follow-the-regularized-leader that obtains regret of order $\min\{σ_{\max}\ln T, \sqrt{d_{\mathrm{tot}}}\}$, where $σ_{\max}$ is the maximum number of missing observations. We then consider exp-concave losses and extend the Online Newton Step algorithm to handle delays with an adaptive learning rate tuning, achieving regret $\min\{d_{\max} n\ln T, \sqrt{d_{\mathrm{tot}}}\}$ where $n$ is the dimension. To our knowledge, this is the first algorithm to achieve such a regret bound for exp-concave losses. We further consider the problem of unconstrained online linear regression and achieve a similar guarantee by designing a variant of the Vovk-Azoury-Warmuth forecaster with a clipping trick. Finally, we implement our algorithms and conduct experiments under various types of delay and losses, showing an improved performance over existing methods.

cs.LG↗

arXiv2025

Complexity and Manipulation of International Kidney Exchange Programmes with Country-Specific Parameters

Kidney Exchange Programmes (KEPs) facilitate the exchange of kidneys, and larger pools of recipient-donor pairs tend to yield proportionally more transplants, leading to the proposal of international KEPs (IKEPs). However, as studied by \citet{mincu2021ip}, practical limitations must be considered in IKEPs to ensure that countries remain willing to participate. Thus, we study IKEPs with country-specific parameters, represented by a tuple $Γ$, restricting the selected transplants to be feasible for the countries to conduct, e.g., imposing an upper limit on the number of consecutive exchanges within a country's borders. We provide a complete complexity dichotomy for the problem of finding a feasible (according to the constraints given by $Γ$) cycle packing with the maximum number of transplants, for every possible $Γ$. We also study the potential for countries to misreport their parameters to increase their allocation. As manipulation can harm the total number of transplants, we propose a novel individually rational and incentive compatible mechanism $\mathcal{M}_{\text{order}}$. We first give a theoretical approximation ratio for $\mathcal{M}_{\text{order}}$ in terms of the number of transplants, and show that the approximation ratio of $\mathcal{M}_{\text{order}}$ is asymptotically optimal. We then use simulations which suggest that, in practice, the performance of $\mathcal{M}_{\text{order}}$ is significantly better than this worst-case ratio.

cs.GT↗

arXiv2025

Toward a Better Understanding of Probabilistic Delta Debugging

Given a list L of elements and a property that L exhibits, ddmin is a well-known test input minimization algorithm designed to automatically eliminate irrelevant elements from L. This algorithm is extensively adopted in test input minimization and software debloating. Recently, ProbDD, an advanced variant of ddmin, has been proposed and achieved state-of-the-art performance. Employing Bayesian optimization, ProbDD predicts the likelihood of each element in L being essential, and statistically decides which elements and how many should be removed each time. Despite its impressive results, the theoretical probabilistic model of ProbDD is complex, and the specific factors driving its superior performance have not been investigated. In this paper, we conduct the first in-depth theoretical analysis of ProbDD, clarifying trends in probability and subset size changes while simplifying the probability model. Complementing this analysis, we perform empirical experiments, including success rate analysis, ablation studies, and analysis on trade-offs and limitations, to better understand and demystify this state-of-the-art algorithm. Our success rate analysis shows how ProbDD addresses bottlenecks of ddmin by skipping inefficient queries that attempt to delete complements of subsets and previously tried subsets. The ablation study reveals that randomness in ProbDD has no significant impact on efficiency. Based on these findings, we propose CDD, a simplified version of ProbDD, reducing complexity in both theory and implementation. Besides, the performance of CDD validates our key findings. Comprehensive evaluations across 76 benchmarks in test input minimization and software debloating show that CDD can achieve the same performance as ProbDD despite its simplification. These insights provide valuable guidance for future research and applications of test input minimization algorithms.

cs.SE↗

arXiv2025

Contextual Linear Bandits with Delay as Payoff

A recent work by Schlisselberg et al. (2024) studies a delay-as-payoff model for stochastic multi-armed bandits, where the payoff (either loss or reward) is delayed for a period that is proportional to the payoff itself. While this captures many real-world applications, the simple multi-armed bandit setting limits the practicality of their results. In this paper, we address this limitation by studying the delay-as-payoff model for contextual linear bandits. Specifically, we start from the case with a fixed action set and propose an efficient algorithm whose regret overhead compared to the standard no-delay case is at most $DΔ_{\max}\log T$, where $T$ is the total horizon, $D$ is the maximum delay, and $Δ_{\max}$ is the maximum suboptimality gap. When payoff is loss, we also show further improvement of the bound, demonstrating a separation between reward and loss similar to Schlisselberg et al. (2024). Contrary to standard linear bandit algorithms that construct least squares estimator and confidence ellipsoid, the main novelty of our algorithm is to apply a phased arm elimination procedure by only picking actions in a volumetric spanner of the action set, which addresses challenges arising from both payoff-dependent delays and large action sets. We further extend our results to the case with varying action sets by adopting the reduction from Hanna et al. (2023). Finally, we implement our algorithm and showcase its effectiveness and superior performance in experiments.

cs.LG↗