Minimax Optimal Strategy for Delayed Observations in Online Reinforcement Learning

We study reinforcement learning with delayed state observation, where the agent observes the current state after some random number of time steps. We propose an algorithm that combines the augmentation method and the upper confidence bound approach. For tabular Markov decision processes (MDPs), we derive a regret bound of $\tilde{\mathcal{O}}(H \sqrt{D_{\max} SAK})$, where $S$ and $A$ are the cardinalities of the state and action spaces, $H$ is the time horizon, $K$ is the number of episodes, and $D_{\max}$ is the maximum length of the delay. We also provide a matching lower bound up to logarithmic factors, showing the optimality of our approach. Our analytical framework formulates this problem as a special case of a broader class of MDPs, where their transition dynamics decompose into a known component and an unknown but structured component. We establish general results for this abstract setting, which may be of independent interest.

Revisiting the Bertrand Paradox via Equilibrium Analysis of No-regret Learners

We study the discrete Bertrand pricing game with a non-increasing demand function. The game has $n \ge 2$ players who simultaneously choose prices from the set $\{1/k, 2/k, \ldots, 1\}$, where $k\in\mathbb{N}$. The player who sets the lowest price captures the entire demand; if multiple players tie for the lowest price, they split the demand equally. We study the Bertrand paradox, where classical theory predicts low prices, yet real markets often sustain high prices. To understand this gap, we analyze a repeated-game model in which firms set prices using no-regret learners. Our goal is to characterize the equilibrium outcomes that can arise under different no-regret learning guarantees. We are particularly interested in questions such as whether no-external-regret learners can converge to undesirable high-price outcomes, and how stronger guarantees such as no-swap regret shape the emergence of competitive low-price behavior. We address these and related questions through a theoretical analysis, complemented by experiments that support the theory and reveal surprising phenomena for no-swap regret learners.

Efficient Uncoupled Learning Dynamics with $\tilde{O}\!\left(T^{-1/4}\right)$ Last-Iterate Convergence in Bilinear Saddle-Point Problems over Convex Sets under Bandit Feedback

In this paper, we study last-iterate convergence of learning algorithms in bilinear saddle-point problems, a preferable notion of convergence that captures the day-to-day behavior of learning dynamics. We focus on the challenging setting where players select actions from compact convex sets and receive only bandit feedback. Our main contribution is the design of an uncoupled learning algorithm that guarantees last-iterate convergence to the Nash equilibrium with high probability. We establish a convergence rate of $\tilde{O}(T^{-1/4})$ up to polynomial factors in problem parameters. Crucially, our proposed algorithm is computationally efficient, requiring only an efficient linear optimization oracle over the players' compact action sets. The algorithm is obtained by combining techniques from experimental design and the classic Follow-The-Regularized-Leader (FTRL) framework, with a carefully chosen regularizer function tailored to the geometry of the action set of each learner.

Improved Regret Bounds for Linear Bandits with Heavy-Tailed Rewards

We study stochastic linear bandits with heavy-tailed rewards, where the rewards have a finite $(1+\epsilon)$-absolute central moment bounded by $\upsilon$ for some $\epsilon \in (0,1]$. We improve both upper and lower bounds on the minimax regret compared to prior work. When $\upsilon = \mathcal{O}(1)$, the best prior known regret upper bound is $\tilde{\mathcal{O}}(d T^{\frac{1}{1+\epsilon}})$. While a lower with the same scaling has been given, it relies on a construction using $\upsilon = \mathcal{O}(d)$, and adapting the construction to the bounded-moment regime with $\upsilon = \mathcal{O}(1)$ yields only a $\Omega(d^{\frac{\epsilon}{1+\epsilon}} T^{\frac{1}{1+\epsilon}})$ lower bound. This matches the known rate for multi-armed bandits and is generally loose for linear bandits, in particular being $\sqrt{d}$ below the optimal rate in the finite-variance case ($\epsilon = 1$). We propose a new elimination-based algorithm guided by experimental design, which achieves regret $\tilde{\mathcal{O}}(d^{\frac{1+3\epsilon}{2(1+\epsilon)}} T^{\frac{1}{1+\epsilon}})$, thus improving the dependence on $d$ for all $\epsilon \in (0,1)$ and recovering a known optimal result for $\epsilon = 1$. We also establish a lower bound of $\Omega(d^{\frac{2\epsilon}{1+\epsilon}} T^{\frac{1}{1+\epsilon}})$, which strictly improves upon the multi-armed bandit rate and highlights the hardness of heavy-tailed linear bandit problems. For finite action sets, we derive similarly improved upper and lower bounds for regret. Finally, we provide action set dependent regret upper bounds showing that for some geometries, such as $l_p$-norm balls for $p \le 1 + \epsilon$, we can further reduce the dependence on $d$, and we can handle infinite-dimensional settings via the kernel trick, in particular establishing new regret bounds for the Mat\'ern kernel that are the first to be sublinear for all $\epsilon \in (0, 1]$.

Learning to Incentivize in Repeated Principal-Agent Problems with Adversarial Agent Arrivals

We initiate the study of a repeated principal-agent problem over a finite horizon $T$, where a principal sequentially interacts with $K\geq 2$ types of agents arriving in an adversarial order. At each round, the principal strategically chooses one of the $N$ arms to incentivize for an arriving agent of unknown type. The agent then chooses an arm based on its own utility and the provided incentive, and the principal receives a corresponding reward. The objective is to minimize regret against the best incentive in hindsight. Without prior knowledge of agent behavior, we show that the problem becomes intractable, leading to linear regret. We analyze two key settings where sublinear regret is achievable. In the first setting, the principal knows the arm each agent type would select greedily for any given incentive. Under this setting, we propose an algorithm that achieves a regret bound of $O(\min\{\sqrt{KT\log N},K\sqrt{T}\})$ and provide a matching lower bound up to a $\log K$ factor. In the second setting, an agent's response varies smoothly with the incentive and is governed by a Lipschitz constant $L\geq 1$. Under this setting, we show that there is an algorithm with a regret bound of $\tilde{O}((LN)^{1/3}T^{2/3})$ and establish a matching lower bound up to logarithmic factors. Finally, we extend our algorithmic results for both settings by allowing the principal to incentivize multiple arms simultaneously in each round.

Stow: Robotic Packing of Items into Fabric Pods

This paper presents a compliant manipulation system capable of placing items onto densely packed shelves. The wide diversity of items and strict business requirements for high producing rates and low defect generation have prohibited warehouse robotics from performing this task. Our innovations in hardware, perception, decision-making, motion planning, and control have enabled this system to perform over 500,000 stows in a large e-commerce fulfillment center. The system achieves human levels of packing density and speed while prioritizing work on overhead shelves to enhance the safety of humans working alongside the robots.

Efficient Near-Optimal Algorithm for Online Shortest Paths in Directed Acyclic Graphs with Bandit Feedback Against Adaptive Adversaries

In this paper, we study the online shortest path problem in directed acyclic graphs (DAGs) under bandit feedback against an adaptive adversary. Given a DAG $G = (V, E)$ with a source node $v_{\mathsf{s}}$ and a sink node $v_{\mathsf{t}}$, let $X \subseteq \{0,1\}^{|E|}$ denote the set of all paths from $v_{\mathsf{s}}$ to $v_{\mathsf{t}}$. At each round $t$, we select a path $\mathbf{x}_t \in X$ and receive bandit feedback on our loss $\langle \mathbf{x}_t, \mathbf{y}_t \rangle \in [-1,1]$, where $\mathbf{y}_t$ is an adversarially chosen loss vector. Our goal is to minimize regret with respect to the best path in hindsight over $T$ rounds. We propose the first computationally efficient algorithm to achieve a near-minimax optimal regret bound of $\tilde O(\sqrt{|E|T\log |X|})$ with high probability against any adaptive adversary, where $\tilde O(\cdot)$ hides logarithmic factors in the number of edges $|E|$. Our algorithm leverages a novel loss estimator and a centroid-based decomposition in a nontrivial manner to attain this regret bound. As an application, we show that our algorithm for DAGs provides state-of-the-art efficient algorithms for $m$-sets, extensive-form games, the Colonel Blotto game, shortest walks in directed graphs, hypercubes, and multi-task multi-armed bandits, achieving improved high-probability regret guarantees in all these settings.

Active learning of neural population dynamics using two-photon holographic optogenetics

Recent advances in techniques for monitoring and perturbing neural populations have greatly enhanced our ability to study circuits in the brain. In particular, two-photon holographic optogenetics now enables precise photostimulation of experimenter-specified groups of individual neurons, while simultaneous two-photon calcium imaging enables the measurement of ongoing and induced activity across the neural population. Despite the enormous space of potential photostimulation patterns and the time-consuming nature of photostimulation experiments, very little algorithmic work has been done to determine the most effective photostimulation patterns for identifying the neural population dynamics. Here, we develop methods to efficiently select which neurons to stimulate such that the resulting neural responses will best inform a dynamical model of the neural population activity. Using neural population responses to photostimulation in mouse motor cortex, we demonstrate the efficacy of a low-rank linear dynamical systems model, and develop an active learning procedure which takes advantage of low-rank structure to determine informative photostimulation patterns. We demonstrate our approach on both real and synthetic data, obtaining in some cases as much as a two-fold reduction in the amount of data required to reach a given predictive power. Our active stimulation design method is based on a novel active learning procedure for low-rank regression, which may be of independent interest.

Overcoming the Sim-to-Real Gap: Leveraging Simulation to Learn to Explore for Real-World RL

In order to mitigate the sample complexity of real-world reinforcement learning, common practice is to first train a policy in a simulator where samples are cheap, and then deploy this policy in the real world, with the hope that it generalizes effectively. Such \emph{direct sim2real} transfer is not guaranteed to succeed, however, and in cases where it fails, it is unclear how to best utilize the simulator. In this work, we show that in many regimes, while direct sim2real transfer may fail, we can utilize the simulator to learn a set of \emph{exploratory} policies which enable efficient exploration in the real world. In particular, in the setting of low-rank MDPs, we show that coupling these exploratory policies with simple, practical approaches -- least-squares regression oracles and naive randomized exploration -- yields a polynomial sample complexity in the real world, an exponential improvement over direct sim2real transfer, or learning without access to a simulator. To the best of our knowledge, this is the first evidence that simulation transfer yields a provable gain in reinforcement learning in settings where direct sim2real transfer fails. We validate our theoretical results on several realistic robotic simulators and a real-world robotic sim2real task, demonstrating that transferring exploratory policies can yield substantial gains in practice as well.

Cost-Effective Proxy Reward Model Construction with On-Policy and Active Learning

Reinforcement learning with human feedback (RLHF), as a widely adopted approach in current large language model pipelines, is \textit{bottlenecked by the size of human preference data}. While traditional methods rely on offline preference dataset constructions, recent approaches have shifted towards online settings, where a learner uses a small amount of labeled seed data and a large pool of unlabeled prompts to iteratively construct new preference data through self-generated responses and high-quality reward/preference feedback. However, most current online algorithms still focus on preference labeling during policy model updating with given feedback oracles, which incurs significant expert query costs. \textit{We are the first to explore cost-effective proxy reward oracles construction strategies for further labeling preferences or rewards with extremely limited labeled data and expert query budgets}. Our approach introduces two key innovations: (1) on-policy query to avoid OOD and imbalance issues in seed data, and (2) active learning to select the most informative data for preference queries. Using these methods, we train a evaluation model with minimal expert-labeled data, which then effectively labels nine times more preference pairs for further RLHF training. For instance, our model using Direct Preference Optimization (DPO) gains around over 1% average improvement on AlpacaEval2, MMLU-5shot and MMLU-0shot, with only 1.7K query cost. Our methodology is orthogonal to other direct expert query-based strategies and therefore might be integrated with them to further reduce query costs.