arXiv subjects

Haipeng Luo

Publications and source records attributed to Haipeng Luo.

At least 19 recordsLinked to original sources

arXiv2026

Group Distributionally Robust Optimization with Flexible Sample Queries

Group distributionally robust optimization (GDRO) aims to learn models that perform well across $m$ distributions simultaneously. Existing methods either (i) query $m$ samples per round, which imposes strict implementation requirements, or (ii) query only a single sample per round, which requires many rounds to converge and therefore leads to long runtime. To avoid these limitations, we introduce a novel setting called \emph{flexible sample queries} (FSQ), which allows the number of samples that can be queried to vary across rounds. Under the FSQ setting, we cast GDRO as a two-player game: one performs non-oblivious online convex optimization, while the other tackles a non-oblivious prediction with limited advice (PLA) problem. In this game, the first player updates its decision using follow-the-regularized-leader with stochastic gradients. For the second player, we develop a new PLA method equipped with an adaptive exploration strategy that can leverage an arbitrary per-round sample size. We then establish the \emph{first} high-probability regret bound for non-oblivious PLA. By integrating these components, we develop an anytime GDRO algorithm that supports FSQ, and derive a high-probability optimization error bound of $O\left(\frac{1}{t}\sqrt{\sum_{j=1}^t \frac{m}{r_j}\log m}\right)$, where $r_j$ is the sample size at round $j$. This result demonstrates that the optimization error decreases as the per-round sample sizes increase, and implies the same near-optimal sample complexity of $O(m\log (m)/ε^2)$ for any fixed sample size $r\in[m]$.

cs.LG↗

arXiv2026

Near-Optimal $\sqrt{K}$-Regret for Online Learning in Uninformed Markov Games

We study online learning in two-player uninformed Markov games, where the opponent may follow an arbitrary, unknown policy in each episode and the learner does not observe the opponent's actions. [TWYS21] showed that achieving sublinear external regret requires an exponential dependence on the episode length $H$. Motivated by this limitation, they studied the weaker notion of Nash-value regret and obtained an $\widetilde{O}(K^{2/3})$ regret bound, where $K$ is the number of episodes. More recently, [LLZR26] introduced a stronger notion called empirical Nash-value regret and achieved an $\widetilde{O}(\sqrt{K})$ bound when the opponent's non-stationarity is moderate, including the case where the opponent follows a fixed policy. However, whether the $\sqrt{K}$ rate is achievable in the worst case remained open. In this paper, we resolve this open question by developing an algorithm that achieves $\widetilde{O}(H^{3/2}S\sqrt{AK})$ empirical Nash-value regret against arbitrary opponent policies, where $S$ is the number of states and $A$ is the number of learner's actions. Specifically, our algorithm combines global and local planning by maintaining a collection of candidate predictions of future losses, each associated with a policy. Global planning learns which candidates to favor across episodes, while local planning combines their policies differently at each state to make decisions. A key ingredient is to coordinate these two components to control the discrepancy between local loss estimates and the total loss of the executed policy, using only the learner's observed trajectories.

cs.LG↗

arXiv2026

Accelerating Min-Max Optimization via Power-Law Stepsizes

We revisit the convergence guarantees of the Extragradient (EG) method for unconstrained biaffine min-max optimization. It is known that EG with a fixed stepsize achieves a $Θ(T^{-1/2})$ last-iterate convergence rate, which is slower than the optimal $\mathcal{O}(T^{-1})$ rate attainable by incorporating additional mechanisms such as anchoring. Motivated by recent advances showing that dynamic stepsizes alone can significantly accelerate gradient descent, we ask whether dynamic stepsizes can similarly accelerate the last-iterate convergence of EG. We present the first positive result in this direction. Specifically, we provide a deterministic dynamic stepsize schedule that accelerates the convergence rate of EG to $\mathcal{O}(T^{-2/3+\varepsilon})$ for any $\varepsilon > 0$. We also show that this rate is nearly tight when the extrapolation and update steps of EG use the same stepsize. We then show that allowing different stepsizes for the extrapolation and update steps further improves the convergence rate to the near-optimal $\mathcal{O}(T^{-1+\varepsilon})$. Our analysis reduces stepsize scheduling to an optimization problem, whose solution leads to a stepsize schedule that follows (a discretization of) a power-law distribution. Our proposed stepsize schedules and analysis extend to other methods, such as Optimistic Gradient (OG), and suggest broader applicability to general min-max optimization problems.

math.OC↗

arXiv2026

Near-Optimal First-Order Regret for Bandits with Feedback Graphs

We study first-order regret guarantees for adversarial bandits with a fixed, known directed feedback graph. For strongly observable graphs, [ACBDK15] establishes a minimax regret of $\widetildeΘ(\sqrt{αT})$, where $α$ denotes the independence number of the graph and $T$ denotes the horizon. On the other hand, the best existing first-order bound scales as $\widetilde{O}(\sqrt{(κ+1) L^\star})$ [LLZ20], where $κ$ denotes the clique partition number, satisfying $κ+1\geqα$, and $L^\star$ denotes the cumulative loss of the best arm, leaving a gap between the graph dependence in worst-case and first-order guarantees. In this paper, we bridge this gap by obtaining an expected regret bound of $\widetilde{O}(\sqrt{αL^\star}+α)$. Our first result is an algorithm for the special case of self-aware graphs, in which every vertex has a self-loop. The algorithm combines the update of EXP3 [ACBFS02] with a sampling rule inspired by exploration by optimization [LS20]. More specifically, we construct a map whose fixed points yield sampling distributions that control the one-round regret remainder in terms of the learner's loss and the graph's independence number, which is crucial in deriving optimal first-order guarantees. We further show that a sufficiently accurate fixed point can be computed in polynomial time by a geometrically convergent iteration. Finally, we extend the algorithm to general strongly observable graphs and achieve the same $\widetilde{O}(\sqrt{αL^\star}+α)$ guarantee by adapting the two-level aggregation approach of [LLZ20].

cs.LG↗

arXiv2026

Omniprediction for All Mixable Proper Losses and Beyond

Omniprediction concerns the task of making predictions that are simultaneously accurate with respect to different losses. Earlier results by [CV09] show that in an online learning setting, $O(\log(|\mathcal{F}||\mathcal{L}|))$ regret is achievable simultaneously against every predictor in a finite predictor class $\mathcal{F}$ and for every loss in a finite class $\mathcal{L}$ of mixable proper losses, while recent advances [OKK25, FP26] show that $\widetilde{O}(\sqrt{T\log(|\mathcal{F}||\mathcal{L}|)})$ regret is achievable simultaneously for every loss in a finite class $\mathcal{L}$ of bounded losses. In this work, we ask whether sublinear regret remains possible when $\mathcal{L}$ is an infinite class of proper losses. Our first result gives a negative answer in general: even when $\mathcal{F}$ contains only two linear predictors, it is impossible to achieve sublinear regret simultaneously for all bounded proper losses. We then show that $\widetilde{O}(T^{1/3}(\log|\mathcal{F}|)^{2/3})$ regret is achievable simultaneously for \textit{all} mixable proper losses and that this bound is optimal up to logarithmic factors. This optimal rate stands in stark contrast to the constant (in $T$) regret achievable for a finite class of mixable proper losses. Finally, we extend our algorithm to obtain a best-of-all-worlds result: in addition to the new regret guarantee for all mixable proper losses, the resulting algorithm simultaneously achieves the existing guarantees for finite loss classes. With appropriate choices of these finite classes, our algorithm simultaneously achieves constant regret for squared loss and log loss, $\widetilde{O}(T^{1/3}(\log|\mathcal{F}|)^{2/3})$ regret for all mixable proper losses, and $\widetilde{O}(\sqrt{T\log|\mathcal{F}|})$ regret for $0$-$1$ loss, all Lipschitz losses, all GLM losses, and other structured families.

cs.LG↗

arXiv2026

From Dueling Bandits to Episodic MDPs: Learning with Adversarial Preference Feedback

In dueling bandits, the learner compares two arms in each round and observes only which one is preferred. This paper asks what changes when the compared pair also affects the next state, as in a recommendation interface where the pair shown to a user affects the user's next context. We formulate this problem as a state-wise preference-based MDP, an episodic tabular MDP in which the learner selects a pair of arms at each visited state, observes only a noisy comparison between them, and moves to a next state that may depend on the pair. The preferences may change adversarially across episodes, and the loss of a pair is defined through Borda scores. We show that the minimax regret of this problem under known transitions is $\tildeΘ(\min\{HT,(H^3SK)^{1/3}T^{2/3}\})$, where $H$, $S$, $K$, and $T$ are the numbers of steps per episode, states, arms, and episodes, and that this rate is achieved by an algorithm based on online linear optimization over the set of occupancy measures. If the pair did not affect the next state, each state would be a separate dueling bandit, and the $T^{2/3}$ term of the minimax regret would be smaller by a factor of $H^{1/3}$, demonstrating the cost of having action-dependent state transitions. We also give a policy optimization algorithm with closed-form updates, whose regret is $\tilde{O}((H^4SK^3)^{1/3}T^{2/3})$ up to lower-order terms, and we extend both algorithms to unknown transitions.

cs.LG↗

arXiv2026

Optimal Nonparametric Dynamic Pricing with Censored Demand and Adversarial Inventory

We study online dynamic pricing with censored demand, where an arbitrary inventory level is revealed before pricing and may adapt to past observations, while demand follows an unknown, price-dependent distribution that is stationary over time. For a horizon of $T$ rounds, Xu et al. [2026] achieved $\widetilde{\mathcal{O}}(\sqrt{T})$ regret under restrictive structural assumptions including linear demand, price-independent additive noise, and conditions relating inventory levels to the noise support. Our first contribution is to extend this framework to a substantially more general and statistically harder nonparametric setting, requiring only the natural assumption that expected sales are nonincreasing in price and allowing nonlinear demand curves and price-dependent noise. For this model, we first propose a simple baseline, Double-Grid-UCB, which discretizes both price and inventory and achieves $\widetilde{\mathcal{O}}(T^{3/4})$ expected regret using separate revenue estimates for each price-inventory grid pair. Then, we develop Threshold-UCB, which improves the expected regret to $\widetilde{\mathcal{O}}(T^{2/3})$. Unlike Double-Grid-UCB, Threshold-UCB reuses sales observations across inventory levels through shared estimates of demand-tail probabilities, allowing the same data to support revenue upper bounds for multiple inventories rather than a single inventory bin. We also complement this upper bound with an $Ω(T^{2/3})$ lower bound via a reduction from stochastic posted pricing, establishing its minimax optimality. Finally, extensive experiments across inventory processes, demand functions, and noise models demonstrate consistently superior performance of Threshold-UCB over benchmark algorithms.

cs.LG↗

arXiv2026

Hunyuan-A13B Technical Report

We present Hunyuan-A13B, an open-source large language model based on a Mixture-of-Experts architecture. It contains 80 billion total parameters but activates only 13 billion during inference, balancing model capability, computational efficiency, and deployment cost. The model is pretrained on a rigorously filtered 20T-token corpus with enhanced STEM data curation, improving factual reliability and reasoning ability. High-quality supervised fine-tuning and large-scale reinforcement learning further enhance its overall performance. Hunyuan-A13B also introduces a dual-mode Chain-of-Thought framework that adapts reasoning depth to task complexity: fast thinking for routine queries and slow thinking for complex, multi-step problems. Evaluations show competitive performance across mathematics, science, programming, general language understanding, and agent tasks, often approaching that of much larger models. Its high inference throughput makes it suitable for latency-sensitive applications. We release Hunyuan-A13B to support open research and practical LLM deployment.

cs.AI↗

arXiv2026

STARE: Surprisal-Guided Token-Level Advantage Reweighting for Policy Entropy Stability

Reinforcement Learning with Verifiable Rewards algorithms like GRPO have emerged as the dominant post-training paradigm for complex reasoning in LLMs, yet commonly suffer from policy entropy collapse during training. We conduct a first-order gradient analysis of token-level entropy dynamics under GRPO and identify a token-level credit assignment mismatch: the per-token entropy variation decomposes into the product of the trajectory-level advantage and an entropy sensitivity function over the next-token distribution, yielding an advantage-surprisal four-quadrant structure and a near-criticality property. Motivated by it, we propose STARE (Surprisal-guided Token-level Advantage Reweighting for policy Entropy stability), which identifies entropy-critical token subsets via batch-internal surprisal quantiles, selectively reweights their effective advantages, and incorporates a target-entropy closed-loop gate for stable entropy regulation. Across model scales from 1.5B to 32B and three task families (Short CoT, Long CoT, and Multi-Turn Tool Use), STARE sustains stable RL training over thousands of steps while maintaining policy entropy within the target band. On AIME24 and AIME25, STARE outperforms DAPO and other competitive baselines by 4%-8% in average accuracy, with reflection tokens and response length growing in tandem, indicating sustained exploration-exploitation balance that further unlocks RL training potential.Code is available at https://github.com/hp-luo/STARE.

cs.LG↗

arXiv2026

Toward Simultaneously Optimal Regret in U-Calibration

U-calibration studies online forecasting algorithms whose predictions can be consumed by any unknown downstream agent, guaranteeing sublinear regret simultaneously for all proper loss functions. Existing U-calibration algorithms achieve worst-case optimal $O(\sqrt{T})$ regret for every bounded proper loss, but they fail to adapt to easier losses: as we show, even for smooth losses such as squared loss, they incur $Ω(\sqrt{T})$ regret instead of the optimal $O(\log T)$ regret. In this work, we show that this limitation is not inherent. Specifically, we design a single forecast algorithm that simultaneously achieves $\tilde O(\sqrt{T})$ regret for every bounded proper loss and $O(\log T)$ regret for every bounded smooth proper loss. More generally, our algorithm also attains logarithmic regret for losses that are smooth relative to the log-barrier, which include several non-Lipschitz examples. Our approach is based on a novel variant of Follow-the-Perturbed-Leader (FTPL) in which perturbations are applied directly in the prediction space using self-concordant noise. The resulting analysis also departs substantially from prior FTPL analyses due to the complex nature of this noise and may be of independent interest.

stat.ML↗

arXiv2026

Adaptive Calibration in Non-Stationary Environments

Making calibrated online predictions is a central challenge in modern AI systems. Much of the existing literature focuses on fully adversarial environments where outcomes may be arbitrary, leading to conservative algorithms that can perform suboptimally in more benign settings, such as when outcomes are nearly stationary. This gap raises a natural question: can we design online prediction algorithms whose calibration error automatically adapts to the degree of non-stationarity in the environment, smoothly interpolating between i.i.d. and adversarial regimes? We answer this question in the affirmative and develop a suite of algorithms that achieve adaptive calibration guarantees under multiple calibration measures. Specifically, with $T$ being the number of rounds, $K$ being the unknown number of i.i.d. segments of the environment, and $C\in[0,T]$ being another unknown non-stationary measure defined as the minimal $\ell_1$ deviation of the mean outcomes, our algorithms attain $\widetilde{O}(\min\{\sqrt{T}+(TC)^{\frac{1}{3}}, \sqrt{KT}\})$ for $\ell_1$ calibration error and $\widetilde{O}(\min\{(1+C)^{\frac{1}{3}}, K\})$ for both $\ell_2$ and pseudo KL calibration error. These bounds match the optimal rates in the stationary case ($C=0$ and $K=1$) and recover known guarantees in the fully adversarial regime ($C, K=Ω(T)$). Our approach builds on and extends prior work [Hu et al., 2026, Luo et al., 2025], introducing an epoch-based scheduling together with a novel non-uniform partition of the prediction space that allocates finer resolution near the underlying ground truth.

cs.LG↗

arXiv2026

Swap Regret Minimization Through Response-Based Approachability

We consider the problem of minimizing different notions of swap regret in online optimization. These forms of regret are tightly connected to correlated equilibrium concepts in games, and have been more recently shown to guarantee non-manipulability against strategic adversaries. The only computationally efficient algorithm for minimizing linear swap regret over a general convex set in $\mathbb{R}^d$ was developed recently by Daskalakis, Farina, Fishelson, Pipis, and Schneider (STOC '25). However, it incurs a highly suboptimal regret bound of $Ω(d^4 \sqrt{T})$ and also relies on computationally intensive calls to the ellipsoid algorithm at each iteration. In this paper, we develop a significantly simpler, computationally efficient algorithm that guarantees $O(d \sqrt{T})$ linear swap regret for a general convex set that has been preconditioned via the John ellipsoid. Our algorithm leverages the powerful response-based approachability framework of Bernstein and Shimkin (JMLR~'15) -- previously overlooked in the line of work on swap regret minimization -- and simultaneously minimizes profile swap regret, which was recently shown to guarantee non-manipulability. Moreover, we establish a matching information-theoretic lower bound: any learner must incur in expectation $Ω(d \sqrt{T})$ linear swap regret for large enough $T$, even when the set is centrally symmetric. This also shows that the classic algorithm of Gordon, Greenwald, and Marks (ICML '08) is existentially optimal for minimizing linear swap regret, although it is computationally inefficient. Finally, we extend our approach to minimize regret with respect to the set of swap deviations with polynomial dimension, unifying and strengthening recent results in equilibrium computation and online learning.

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

One Good Source is All You Need: Near-Optimal Regret for Bandits under Heterogeneous Noise

We study $K$-armed Multiarmed Bandit (MAB) problem with $M$ heterogeneous data sources, each exhibiting unknown and distinct noise variances $\{σ_j^2\}_{j=1}^M$. The learner's objective is standard MAB regret minimization, with the additional complexity of adaptively selecting which data source to query from at each round. We propose Source-Optimistic Adaptive Regret minimization (SOAR), a novel algorithm that quickly prunes high-variance sources using sharp variance-concentration bounds, followed by a `balanced min-max LCB-UCB approach' that seamlessly integrates the parallel tasks of identifying the best arm and the optimal (minimum-variance) data source. Our analysis shows SOAR achieves an instance-dependent regret bound of $\tilde{O}\left({σ^*}^2\sum_{i=2}^K \frac{\log T}{Δ_i} + \sqrt{K \sum_{j=1}^M σ_j^2}\right)$, up to preprocessing costs depending only on problem parameters, where ${σ^*}^2 := \min_j σ_j^2$ is the minimum source variance and $Δ_i$ denotes the suboptimality gap of the $i$-th arm. This result is both surprising as despite lacking prior knowledge of the minimum-variance source among $M$ alternatives, SOAR attains the optimal instance-dependent regret of standard single-source MAB with variance ${σ^*}^2$, while incurring only an small (and unavoidable) additive cost of $\tilde O(\sqrt{K \sum_{j=1}^M σ_j^2})$ towards the optimal (minimum variance) source identification. Our theoretical bounds represent a significant improvement over some proposed baselines, e.g. Uniform UCB or Explore-then-Commit UCB, which could potentially suffer regret scaling with $σ_{\max}^2$ in place of ${σ^*}^2$-a gap that can be arbitrarily large when $σ_{\max} \gg σ^*$. Experiments on multiple synthetic problem instances and the real-world MovieLens\;25M dataset, demonstrating the superior performance of SOAR over the baselines.

cs.LG↗

arXiv2026

Calibeating Made Simple

We study calibeating, the problem of post-processing external forecasts online to minimize cumulative losses and match an informativeness-based benchmark. Unlike prior work, which analyzed calibeating for specific losses with specific arguments, we reduce calibeating to existing online learning techniques and obtain results for general proper losses. More concretely, we first show that calibeating is minimax-equivalent to regret minimization. This recovers the $O(\log T)$ calibeating rate of Foster and Hart [FH23] for the Brier and log losses and its optimality, and yields new optimal calibeating rates for mixable losses and general bounded losses. Second, we prove that multi-calibeating is minimax-equivalent to the combination of calibeating and the classical expert problem. This yields new optimal multi-calibeating rates for mixable losses, including Brier and log losses, and general bounded losses. Finally, we obtain new bounds for achieving calibeating and calibration simultaneously for the Brier loss. For binary predictions, our result gives the first calibrated algorithm that at the same time also achieves the optimal $O(\log T)$ calibeating rate.

cs.LG↗

arXiv2026

Automatic Link Selection in Multi-Channel Multiple Access with Link Failures

This paper focuses on the problem of automatic link selection in multi-channel multiple access control using bandit feedback. In particular, a controller assigns multiple users to multiple channels in a time-slotted system, where in each time slot, at most one user can be assigned to a given channel, and at most one channel can be assigned to a given user. Given that user $i$ is assigned to channel $j$, the transmission fails with a fixed unknown probability $1-q_{i,j}$. The assignments are made dynamically using success/failure feedback. The goal is to maximize the time-average utility, where we consider an arbitrary (possibly nonsmooth) concave, entrywise nondecreasing utility function. The first proposed algorithm has fast $\mathcal{O}(\sqrt{\log(T)/T})$ convergence. However, this algorithm requires solving a convex optimization problem within each iteration, which can be computationally expensive. The second algorithm has slower $\mathcal{O}(\sqrt[3]{\log(T)/T})$ convergence, while avoiding the costly inner optimization. Both of these algorithms are adaptive. In particular, the convergence guarantee holds for any interval of $T$ consecutive slots during which the success probabilities do not change. We further study several special cases. In the single-channel setting, we obtain both fast $\mathcal{O}(\sqrt{\log(T)/T})$ convergence and efficient implementation via a simpler adaptive mechanism. We also consider a UCB-based non-adaptive algorithm with max-weight-type decisions. Simulations highlight intriguing performance trade-offs and demonstrate rapid adaptation of the proposed adaptive schemes.

eess.SY↗

arXiv2026

A Short Note on a Variant of the Squint Algorithm

This short note describes a simple variant of the Squint algorithm of Koolen and Van Erven [2015] for the classic expert problem. Via an equally simple modification of their proof, we prove that this variant ensures a regret bound that resembles the one shown in a recent work by Freund et al. [2026] for a variant of the NormalHedge algorithm [Chaudhuri et al., 2009].

cs.LG↗

arXiv2026

AgentMath: Empowering Mathematical Reasoning for Large Language Models via Tool-Augmented Agent

Large Reasoning Models (LRMs) like o3 and DeepSeek-R1 have achieved remarkable progress in reasoning tasks with long cot. However, they remain computationally inefficient and struggle with accuracy when solving problems requiring complex mathematical operations. In this work, we present AgentMath, an agent framework that seamlessly integrates language models' reasoning capabilities with code interpreters' computational precision to efficiently tackle complex mathematical problems. Our approach introduces three key innovations: (1) An automated method that converts natural language chain-of-thought into structured tool-augmented trajectories, generating high-quality supervised fine-tuning (SFT) data to alleviate data scarcity; (2) A novel agentic reinforcement learning (RL) paradigm that dynamically interleaves natural language generation with real-time code execution. This enables models to autonomously learn optimal tool-use strategies through multi-round interactive feedback, while fostering emergent capabilities in code refinement and error correction; (3) An efficient training system incorporating innovative techniques, including request-level asynchronous rollout scheduling, agentic partial rollout, and prefix-aware weighted load balancing, achieving 4-5x speedup and making efficient RL training feasible on ultra-long sequences with scenarios with massive tool invocation. The evaluations show that AgentMath achieves state-of-the-art performance on challenging mathematical competition benchmarks including AIME24, AIME25, and HMMT25. Specifically, AgentMath-30B-A3B attains 90.6%, 86.4%, and 73.8% accuracy respectively, surpassing OpenAI-o3-mini and Claude-Opus-4.0-Thinking while remaining competitive with OpenAI-o3, Gemini-2.5-Pro, and DeepSeek-R1-671B-0528.These results validate the effectiveness of our approach and pave the way for building scalable mathematical reasoning agents.

cs.AI↗