ICML 2026 Papers

We derive a robust update rule for the online infinite hidden Markov model (iHMM) for when the streaming data contains outliers and the model is misspecified. Leveraging recent advances in generalised Bayesian inference, we define robustness via the posterior influence function (PIF), and provide conditions under which the online iHMM has bounded PIF. Imposing robustness inevitably induces an adaptation lag for regime switching. Our method, which is called Batched Robust iHMM (BR-iHMM), balances adaptivity and robustness with two additional tunable parameters. Across limit order book data, hourly electricity demand, and a synthetic high-dimensional linear system, BR-iHMM reduces one-step-ahead forecasting error by up to 67% relative to competing online Bayesian methods. Together with theoretical guarantees of bounded PIF, our results highlight the practicality of our approach for both forecasting and interpretable online learning.

We give a very general and simple framework to incorporate predictions on requests for online covering problems in a rigorous and black-box manner. Our framework turns any online algorithm with competitive ratio $\rho(k, \cdot)$ depending on $k$, the number of arriving requests, into an algorithm with competitive ratio of $\rho(\eta, \cdot)$, where $\eta$ is the prediction error. With accurate enough prediction, the resulting competitive ratio breaks through the corresponding worst-case online lower bounds, and smoothly degrades as the prediction error grows. This framework directly applies to a wide range of well-studied online covering problems such as facility location, Steiner problems, set cover, parking permit, etc., and yields improved and novel bounds.

We study the problem of neural logistic bandits, where the main task is to learn an unknown reward function within a logistic link function using a neural network. Existing approaches either exhibit unfavorable dependencies on $\kappa$, where $1/\kappa$ represents the minimum variance of reward distributions, or suffer from direct dependence on the feature dimension $d$, which can be huge in neural network–based settings. In this work, we introduce a novel Bernstein-type inequality for self-normalized vector-valued martingales that is designed to bypass a direct dependence on the ambient dimension. This lets us deduce a regret upper bound that grows with the effective dimension $\widetilde{d}$, not the feature dimension, while keeping a minimal dependence on $\kappa$. Based on the concentration inequality, we propose two algorithms, NeuralLog-UCB-1 and NeuralLog-UCB-2, that guarantee regret upper bounds of order $\widetilde{O}(\widetilde{d}\sqrt{\kappa T})$ and $\widetilde{O}(\widetilde{d}\sqrt{T/\kappa})$, respectively, improving on the existing results. Lastly, we report numerical results on both synthetic and real datasets to validate our theoretical findings.

Linear bandits have long been a central topic in online learning, with applications ranging from recommendation systems to adaptive clinical trials. Their general learnability has been established when the objective is to minimise the inner product between a cost parameter and the decision variable. While this is highly general, this reliance on an inner product structure belies the name of \emph{linear} bandits, and fails to account for problems such as Optimal Transport. Using the Kantorovich formulation of Optimal Transport as an example, this article shows that an inner product structure is \emph{not} necessary to achieve efficient learning in linear bandits. We propose a refinement of the classical OFUL algorithm that operates by embedding the action set into a Hilbertian subspace, where confidence sets can be built via least-squares estimation. Actions are then constrained to this subspace by penalising optimism. The analysis is completed by leveraging convergence results from penalised (entropic) transport to the Kantorovich problem. Up to this approximation term, the resulting algorithm achieves the same trajectorial regret upper bounds as the OFUL algorithm, which we turn into worst-case regret using functional regression techniques. Its regret interpolates between $\tilde{\mathcal O}(\sqrt{T})$ and ${\mathcal O}(T)$, depending on the regularity of the cost function, and recovers the parametric rate $\tilde{\mathcal O}(\sqrt{dT})$ in finite-dimensional settings.

Thompson Sampling is one of the most widely used and studied bandit algorithms, known for its simple structure, low regret performance, and solid theoretical guarantees. Yet, in stark contrast to most other families of bandit algorithms, the exact mechanism through which posterior sampling (as introduced by Thompson) is able to "properly" balance exploration and exploitation, remains a mystery. In this paper, we show that the core insight to address this question stems from recasting Thompson Sampling as an online optimization algorithm. To distill this, we introduce a time invariant notion of regret that summarizes cumulative regret across horizons (through a regret bound), leading to a time invariant Bellman-optimal policy. It turns out that Thompson Sampling admits an online optimization form that mimics the structure of the Bellman-optimal policy, where greediness is regularized by a measure of residual uncertainty. When viewed through this new lens of online optimization, Thompson Sampling can be understood and improved in a principled manner, by comparing it against the Bellman-optimal benchmark.

We study hybrid reinforcement learning (RL) in adversarial Markov Decision Processes (MDPs), where the learner simultaneously receives on-policy feedback from the executed policy and off-policy feedback from a fixed behavior policy, and loss functions can change arbitrarily over time. On-policy feedback allows exploration and ensures the worst-case guarantee against any comparator policy, while off-policy feedback provides coverage-dependent guarantee that scales with the "mismatch" between the behavior and comparator policies (called coverage ratio) and can be sharper than on-policy results whenever this ratio is small. We propose a new hybrid RL framework that accommodates adversarial losses and unknown transitions, preserving off-policy guarantees while ensuring non-trivial worst-case performance.

Network routers that enforce Quality-of-Service (QoS) guarantees must decide, at every clock cycle, which expiring packet of information to transmit, even when the value of the packet is unknown until it is processed. We frame this problem as the Online Packet Scheduling with Deadlines (OPSD) problem under Partial Feedback: packets arrive at every clock cycle, with different deadlines, but the weights are only observed after execution. Under a stochastic assumption on the unknown weights, we explore different variants of the OPSD problem with bandit feedback. We establish a connection between our setting and the sleeping bandits problem, and set our learning goal to $\alpha$-regret minimization. We provide algorithms with provable $\alpha$-regret guarantees under different spans of slackness, distinguishing systems allowing for randomization and systems that do not. In every scenario, our algorithms achieve an $\alpha$-regret upper bound of $\widetilde{\mathcal{O}}\left(\sqrt{KT}\right)$, matching the lower bound for the standard bandit setting. In the practically relevant case of $2$-bounded deadline instances, where the deadline is set at most one clock cycle away from the arrival, our deterministic algorithm achieves the provably tightest possible competitive ratio. Remarkably, when the number of distinct packet types $K\ge 2$ is finite, it is possible to break the well-established $\Phi = \frac{1+\sqrt{5}}{2}$ competitive ratio barrier and attain a tighter competitive ratio $\theta_K$ ranging in $[\sqrt{2}, \Phi)$.

Online reinforcement learning in non-episodic, finite-horizon MDPs remains underexplored and is challenged by the need to estimate returns to a fixed terminal time. Existing infinite-horizon methods, which often rely on discounted contraction, do not naturally account for this fixed-horizon structure. We introduce a modified Q-function: rather than targeting the full-horizon, we learn a K-step lookahead Q-function that truncates planning to the next K steps. To further improve sample efficiency, we introduce a thresholding mechanism: actions are selected only when their estimated K-step lookahead value exceeds a time-varying threshold. We provide an efficient tabular learning algorithm for this novel objective, proving it achieves fast finite-sample convergence: it achieves minimax optimal constant regret for $K=1$ and $\mathcal{O}(\max((K-1),C_{K-1})\sqrt{SAT\log(T)})$ regret for any $K \geq 2$. We numerically evaluate the performance of our algorithm under the objective of maximizing reward. Our implementation adaptively increases K over time, balancing lookahead depth against estimation variance. Empirical results demonstrate superior cumulative rewards over state-of-the-art tabular RL methods across synthetic MDPs and RL environments: JumpRiverswim, FrozenLake and AnyTrading. Code is provided on \href{https://github.com/jamie01713/K-Step-Lookahead}{github}.

We propose a unified framework to enhance the power of online multiple hypothesis testing procedures based on $e$-values. While $e$-value-based methods offer robust online False Discovery Rate (FDR) control under minimal assumptions, they often suffer from power loss by discarding evidence that exceeds the rejection threshold. We address this inefficiency via the \textbf{S}equential \textbf{C}ontrol with \textbf{O}vershoot \textbf{R}efund for \textbf{E}-values (SCORE) framework, which leverages the inequality $\mathbb{I}(y \ge 1) \le y - (y-1)_+$, valid for all $y\ge 0$, to reclaim this otherwise ``wasted'' evidence. This simple yet powerful insight yields a unified principle for improving a broad class of online testing algorithms. Building on this framework, we develop SCORE-enhanced versions of several state-of-the-art procedures, including SCORE-LOND, SCORE-LORD, and SCORE-SAFFRON, all of which strictly dominate their original counterparts while preserving valid finite-sample FDR control. Furthermore, under mild assumptions, SCORE permits retroactive updates of alpha‑wealth by using the latest decision twice: first to determine its reward or loss, and then to refresh past wealth. Such a mechanism enables more aggressive testing strategies while maintaining valid FDR control, thereby further improving statistical power. The effectiveness of the proposed methods is validated through extensive simulation and real-data experiments.

In many real-world settings, a centralized decision-maker must repeatedly allocate finite resources to a population over multiple time steps. Individuals who receive a resource derive some stochastic utility; to characterize the population-level effects of an allocation, the expected individual utilities are then aggregated using a social welfare function (SWF). We formalize this setting and present a general confidence sequence framework for SWF-based online learning and inference, valid for any monotonic, concave, and Lipschitz-continuous SWF. Our key insight is that monotonicity alone suffices to lift confidence sequences from individual utilities to anytime-valid bounds on optimal welfare. Building on this foundation, we propose SWF-UCB, a SWF-agnostic online learning algorithm that achieves near-optimal $\tilde{\mathcal{O}}(n+\sqrt{nkT})$ regret (for $k$ resources distributed among $n$ individuals at each of $T$ time steps). We instantiate our framework on three normatively distinct SWF families: Weighted Power Mean, Kolm, and Gini, providing bespoke oracle algorithms for each. Experiments confirm $\sqrt{T}$ scaling and reveal rich interactions between $k$ and SWF parameters. This framework naturally supports inference applications such as sequential hypothesis testing, optimal stopping, and policy evaluation.

We formulate the problem of \emph{exact unlearning} in reinforcement learning, where the goal is to design an efficient framework that enables the removal of any user’s data upon deletion request, i.e., the online learner’s output after unlearning be \emph{indistinguishable} from what would have been produced had the deleted user never interacted with the learner. For any $\rho >0$, we show that there exists a reinforcement learning (RL) algorithm that is $\rho$-TV-stable and supports an exact unlearning procedure whose expected computational cost is only a $\rho \sqrt{\ln T}$ fraction of the computational cost of retraining from scratch. We construct such a $\rho$-TV-stable RL algorithm for tabular Markov decision processes (MDPs), which achieves a regret bound of $\mathcal{O}(H^2 \sqrt{SAT} + H^3 S^2 A + {H^{2.5} S^2 A}/{\rho})$, where $S, A, H$, and $T$ denote the number of states, the number of actions, the episode horizon, and the number of episodes, respectively. We also establish a lower bound of $\Omega(H\sqrt{SAT}+{SAH}/{\rho})$ for $\rho$-TV-stable RL algorithms, showing that our algorithm is nearly minimax optimal.

Addressing Constrained Online Convex Optimization (COCO), we introduce CLASP (Convex Losses And Squared Penalties), a framework that minimizes cumulative loss together with squared constraint violations. We propose two variants of CLASP, CLASP-I and CLASP-F, allowing for a joint or separate handling of the static decision set and the time-varying constraints, a decoupling flexibility that affords simpler implementations when projections onto the static decision set are easy. Our theoretical analysis departs from prior work by fully leveraging the variety of \emph{cutter operators}, and contraction properties such as the strongly quasi-nonexpansiveness, a proof strategy not previously applied in this setting. For convex losses, both CLASP algorithms achieve regret $O\left(T^{\max\\{\beta,1-\beta\\}}\right)$ and cumulative squared penalty $O\left(T^{\\{1-\beta\\}}\right)$ for any $\beta \in (0,1)$. Most importantly, for strongly convex problems, we provide the first logarithmic guarantees on both regret and cumulative squared penalty: In the strongly convex case, both CLASP algorithms guarantee that the regret is upper bounded by $O( \log T )$ and the cumulative squared penalty is also upper bounded by $O( \log T )$.

We study consumer utility maximization in an online random-order model where strategic agents arrive sequentially. To circumvent strong impossibility results for utility maximization, we turn to the framework of learning-augmented mechanism design. Crucially, we show that the types of predictions commonly used in learning-augmented mechanism design (such as predictions of agent values or the optimal value) are not useful for utility maximization, where payments are directly at odds with the objective. Instead, we identify that a qualitatively different kind of prediction suffices: the identity of the highest-valued agent. First, we provide a deterministic truthful mechanism for our online setting by adapting offline randomized techniques. Then, we augment our mechanism with predictions. When the predictions are correct, we achieve a constant approximation to the optimal solution under full information (consistency), and even when predictions are arbitrarily bad, we guarantee a constant approximation to the best implementable solution (robustness).

Recent post-training quantization (PTQ) methods have adopted block rotations to diffuse outliers prior to rounding. While this reduces the overhead of online full-vector rotations, the effect of block structure on outlier suppression remains poorly understood. To fill this gap, we present the first systematic, non-asymptotic analysis of outlier suppression for block Hadamard rotations. Our analysis reveals that outlier suppression is fundamentally limited by the geometry of the input vector. In particular, in the deterministic worst case, post-rotation outliers are minimized when the pre-rotation $\ell_1$ norm mass is evenly distributed across blocks. Guided by these insights, we introduce PeRQ (Permute, Rotate, then Quantize), a PTQ framework that redistributes activation mass via permutations prior to rotation. We propose a greedy mass diffusion algorithm to calibrate permutations by equalizing the expected blockwise $\ell_1$ norms. To avoid adding inference overhead, we identify permutation-equivariant regions in transformer architectures to merge these permutations into model weights before deployment. Experiments show that PeRQ consistently improves accuracy across all block sizes, recovering up to 90% of the full-vector rotation perplexity when quantizing Llama3 1B to INT4 with block size 16, compared to 46% without permutations.

We study the revenue of approximate correlated equilibrium in discrete first price auctions - the set of allowable bids is $\mathcal{B} = \{0, 1/k, \dots, 1 - 1/k, 1\}$ for some $k \in \mathbb{N}$. We show that the revenue of any $\epsilon$-\textit{approximate} correlated equilibrium is at least $v_2 - \Theta(1/k)- \Theta(\epsilon k^2)$, where $v_2 \geq 0$ is the second-highest valuation. Our results establish the first polynomial convergence rates on the revenue generated by no-swap regret bidders in first-price auctions. For instance, if bidders admit the optimal swap regret of $\mathcal{O}(\sqrt{k T})$, then the time-averaged revenue is at least $v_2 - \Theta(1/k) - \Theta(\epsilon)$ after $\mathcal{O}(k^5/\epsilon^2)$ rounds.

While the auto-bidding literature predominantly considers independent bidding, we investigate the coordination problem among multiple auto-bidders in online advertising platforms. Two motivating scenarios are: collaborative bidding among multiple bidders managed by a third-party bidding agent, and strategic bid selection for multiple ad campaigns managed by a single advertiser. We formalize this coordination problem as a theoretical model and investigate the coordination mechanism where only the highest-value bidder competes with outside bidders, while other coordinated bidders refrain from competing. We demonstrate that such a coordination mechanism dominates independent bidding, improving both Return-on-Spend (RoS) compliance and the total value accrued for the participating auto-bidders or ad campaigns, for a broad class of auto-bidding algorithms. Additionally, our simulations on synthetic and real-world datasets support the theoretical result that coordination outperforms independent bidding. These findings highlight both the theoretical potential and the practical robustness of coordinated auto-bidding in online auctions.

Motivated by the recency effect in online learning, we study algorithms for single-pass \emph{sliding-window streaming multi-armed bandits (MABs)} in this paper. In this setting, we are given $n$ arms with unknown sub-Gaussian reward distributions and a parameter $W$. The arms arrive in a single-pass stream, and only the most recent $W$ arms are considered valid. The algorithm is required to perform pure exploration and regret minimization with \emph{limited memory}, \textcolor{red}{defined as the number of stored arms}. The model is a natural extension of the streaming multi-armed bandits model (without the sliding window) that has been extensively studied in recent years. We provide a comprehensive analysis of both the pure exploration and regret minimization problems with the model. For pure exploration, we prove that finding the best arm is hard with sublinear memory while finding an \emph{approximate} best arm admits an efficient algorithm. For regret minimization, we explore a new notion of regret and give sharp memory-regret trade-offs for any single-pass algorithms. We complement our theoretical results with experiments, demonstrating the trade-offs between sample, regret, and memory.

InfoNCE is the standard contrastive learning objective, but its softmax form is not only a computational convenience: it also encodes a statistical assumption about how the top-scoring example is selected. Using extreme value theory, we show that this assumption is often misaligned with the normalized embedding setting used in modern contrastive learning. Motivated by this mismatch, we propose \textsc{WEINCE}, a simple modification of InfoNCE that uses anchor-wise online batch statistics to blend the usual softmax logits with an endpoint shortfall correction, adding no trainable parameters. Across five vision benchmarks, \textsc{WEINCE} yields consistent improvements in frozen-feature evaluation. These results show that a more faithful statistical treatment of hard negatives can improve contrastive objectives.\footnote{Code: \href{https://github.com/hsme98/weince}{github.com/hsme98/weince}.}

We study a learner who sequentially makes and broadcasts predictions of some underlying adversarially varying state. Many downstream decision makers with different goals and different long-term constraints consume these decisions to choose actions. In this setting we give the first algorithm that obtains simultaneous *dynamic regret* guarantees for all of the decision makers --- where regret for each agent is measured against a potentially changing sequence of actions across rounds of interaction, while also ensuring vanishing constraint violation for each agent. We can promise these dynamic regret bounds not just marginally, but simultaneously on many different intersecting subsequences, which lets decision makers compete with strategies that adapt with both long-term drift and short-term variation. Our results do not require the decision makers to maintain any state, but just to react myopically to our predictions.