arXiv subjects

Kevin Jamieson

Publications and source records attributed to Kevin Jamieson.

At least 19 recordsLinked to original sources

arXiv2026

Batched Stochastic Linear Bandits with 1-Bit Communication Constraints

We study stochastic linear bandits under a natural combination of batching and communication constraints: the time horizon is partitioned into batches of equal size $B$, and during each batch the learner sends $B$ requested arm pulls to an agent, who then observes the corresponding $B$ rewards and responds with a single bit of feedback to the learner. For each batch, the learner specifies the 1-bit quantization rule the agent uses, which may depend on all previously received bits but not on any past rewards directly. This setting addresses a significant yet unexplored ``middle ground'' between previous models having per-round quantization only or total bit budgets only. We establish a minimax lower bound showing that $\Omega(B\min\{d,\log\lvert \mathcal{A} \rvert\})$ regret is unavoidable due to the 1-bit communication bottleneck, even in the absence of noise. Combined with standard statistical limits, this yields a general lower bound of $\widetilde{\Omega}(B\min\{d,\log\lvert \mathcal{A} \rvert\} + \sqrt{dT \min\{d,\log\lvert \mathcal{A} \rvert\}})$. We develop two phased-elimination algorithms based on $G$-optimal designs and 1-bit mean estimation. The first achieves $\widetilde{O}(dB + d\sqrt{T})$ regret, matching the lower bound up to logarithmic factors when $\lvert \mathcal{A} \rvert = \exp(\Omega(d))$, and the second incorporates a safe-arm identification and warm-start procedure to obtain $\widetilde{O}(B\log\lvert \mathcal{A} \rvert + d^{3/2}\sqrt{B} + \sqrt{dT\log\lvert \mathcal{A} \rvert})$ regret, which is near-optimal in broad scaling regimes of $(\lvert \mathcal{A} \rvert, B, d, T)$. Together, our results demonstrate that a single bit of feedback per batch suffices to nearly match the minimax regret of unconstrained linear bandits in broad scaling regimes, even for batch sizes as large as $\Theta(\sqrt{T})$.

stat.ML↗

arXiv2026

Near-Optimal Regret in Adversarial Kernel Bandits

We study the adversarial kernel bandit problem, in which the loss at each round is induced by an arbitrary bounded element of a reproducing kernel Hilbert space (RKHS). We propose an exponential-weights algorithm built on a regularized importance-weighted loss estimator, together with an explicit correction term that cancels the bias introduced by the regularization. Our main result bounds the regret by $\widetilde{{O}}\big(\sqrt{T\, d_*(\lambda)\,\log|{X}|}\big)$, where $d_*(\lambda)$ is a widely-adopted notion of effective dimension that captures the complexity of the kernel. Up to logarithmic factors, this matches the known rate achieved in the related stochastic kernel bandit problem. A notable application is the Mat\'ern$(\nu,d)$ kernel with smoothness parameter $\nu$ on $\mathbb{R}^d$, for which our bound specializes to $\widetilde{{O}}\big(T^{(\nu+d)/(2\nu+d)}\big)$, improving over the best-known prior rate of Chatterji et al. [2019] while simultaneously removing the rank-one adversary assumption required by their analysis. Moreover, this rate is the same as the known optimal rate for stochastic kernel bandits, and also matches a lower bound from concurrent work up to a $\log T$ factor.

cs.LG↗

arXiv2026

On the Power of Adaptivity for $\varepsilon$-Best Arm Identification in Linear Bandits

We study the minimax sample complexity of $\varepsilon$-best arm identification in linear bandits. Given a compact action set $\mathcal{X}$ that spans $\mathbb{R}^d$ and an unknown reward vector $\theta\in\mathbb{R}^d$, the goal is to output an arm $\widehat{x}\in\mathcal{X}$ such that $\langle \widehat{x},\theta\rangle \ge \max_{x\in\mathcal{X}} \langle x,\theta\rangle - \varepsilon$ with probability at least $1-\delta$, using as few samples as possible. First, we present a non-adaptive fixed-design method with sample complexity $\mathcal{O}\!\left(\frac{d\log(1/\delta)}{\varepsilon^2}+\frac{w(\mathcal{X})^2}{\varepsilon^2}\right)$, where $w(\mathcal{X})$ is a Gaussian width term dependent on $\mathcal{X}$, and we prove a matching lower bound $\Omega\!\left(\frac{d\log(1/\delta)}{\varepsilon^2}+\frac{w(\mathcal{X})^2}{\varepsilon^2}\right)$ for all non-adaptive fixed-design methods. We then turn to adaptive sampling. We raise an important structural question: beyond the canonical basis, are there structured action sets for which adaptivity yields only logarithmic-factor improvements over the optimal non-adaptive rate? We answer in the affirmative for several natural action sets, namely the hypercube, the $\ell_2$ ball, $m$-sets, and multi-task multi-armed bandits. Finally, we provide the first construction of an action set $\mathcal{X}$ for which adaptivity yields a polynomial-factor improvement over every non-adaptive algorithm. A key ingredient behind this separation is an $\ell_2$-norm estimation subroutine: we design an adaptive algorithm that uses $\mathcal{O}\!\left(\frac{d\log(1/\delta)}{\varepsilon^2}\right)$ samples from the unit $\ell_2$ ball in $\mathbb{R}^d$ and outputs an estimate $\widehat r$ satisfying $|\widehat r-\|\theta\|_2|\le \varepsilon$ with probability at least $1-\delta$, where $\theta$ is the unknown reward vector.

cs.LG↗

arXiv2026

Optimal Posterior Sampling for Policy Identification in Tabular Markov Decision Processes

We study the $(\varepsilon, \delta)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high computational cost, rendering them hard to implement, and also suffer from suboptimal dependence on $\log(1/\delta)$. We propose a randomized and computationally efficient algorithm for best policy identification that combines posterior sampling with an online learning algorithm to guide exploration in the MDP. Our method achieves asymptotic optimality in sample complexity, also in terms of posterior contraction rate, and runs in $O(S^2AH)$ per episode, matching standard model-based approaches. Unlike prior algorithms such as MOCA and PEDEL, our guarantees remain meaningful in the asymptotic regime and avoid sub-optimal polynomial dependence on $\log(1/\delta)$. Our results provide both theoretical insights and practical tools for efficient policy identification in tabular MDPs.

cs.LG↗

arXiv2026

On The Complexity of Best-Arm Identification in Non-Stationary Linear Bandits

We study the fixed-budget best-arm identification (BAI) problem in non-stationary linear bandits. Concretely, given a fixed time budget $T\in \mathbb{N}$, finite arm set $\mathcal{X} \subset \mathbb{R}^d$, and a potentially adversarial sequence of unknown parameters $\lbrace \theta_t\rbrace_{t=1}^{T}$ (hence non-stationary), a learner aims to identify the arm with the largest cumulative reward $x_* = \arg\max_{x \in \mathcal{X}} x^\top\sum_{t=1}^T \theta_t$ with high probability. In this setting, it is well-known that uniformly sampling arms from the G-optimal design yields a minimax-optimal error probability of $\exp\left(-\Theta\left(T / H_{G}\right)\right)$, where $H_{G}$ scales proportionally with the dimension $d$. However, this notion of complexity is overly pessimistic, as it is derived from a lower bound in which the arm set consists only of the standard basis vectors, thus masking any potential advantages arising from arm sets with richer geometric structure. To address this, we establish an arm-set-dependent lower bound that, in contrast, holds for any arm set. Motivated by the ideas underlying our lower bound, we propose the Adjacent-optimal design, a specialization of the well-known $\mathcal{X}\mathcal{Y}$-optimal design, and develop the $\textsf{Adjacent-BAI}$ algorithm. We prove that the error probability of $\textsf{Adjacent-BAI}$ matches our lower bound up to constants, verifying the tightness of our lower bound, and establishing the arm-set-dependent complexity of this setting.

stat.ML↗

arXiv2026

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.

cs.LG↗

arXiv2026

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.

cs.GT↗

arXiv2026

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.

stat.ML↗

arXiv2025

On the Universal Near Optimality of Hedge in Combinatorial Settings

In this paper, we study the classical Hedge algorithm in combinatorial settings. In each round, the learner selects a vector $\boldsymbol{x}_t$ from a set $X \subseteq \{0,1\}^d$, observes a full loss vector $\boldsymbol{y}_t \in \mathbb{R}^d$, and incurs a loss $\langle \boldsymbol{x}_t, \boldsymbol{y}_t \rangle \in [-1,1]$. This setting captures several important problems, including extensive-form games, resource allocation, $m$-sets, online multitask learning, and shortest-path problems on directed acyclic graphs (DAGs). It is well known that Hedge achieves a regret of $O\big(\sqrt{T \log |X|}\big)$ after $T$ rounds of interaction. In this paper, we ask whether Hedge is optimal across all combinatorial settings. To that end, we show that for any $X \subseteq \{0,1\}^d$, Hedge is near-optimal--specifically, up to a $\sqrt{\log d}$ factor--by establishing a lower bound of $\Omega\big(\sqrt{T \log(|X|)/\log d}\big)$ that holds for any algorithm. We then identify a natural class of combinatorial sets--namely, $m$-sets with $\log d \leq m \leq \sqrt{d}$--for which this lower bound is tight, and for which Hedge is provably suboptimal by a factor of exactly $\sqrt{\log d}$. At the same time, we show that Hedge is optimal for online multitask learning, a generalization of the classical $K$-experts problem. Finally, we leverage the near-optimality of Hedge to establish the existence of a near-optimal regularizer for online shortest-path problems in DAGs--a setting that subsumes a broad range of combinatorial domains. Specifically, we show that the classical Online Mirror Descent (OMD) algorithm, when instantiated with the dilated entropy regularizer, is iterate-equivalent to Hedge, and therefore inherits its near-optimal regret guarantees for DAGs.

cs.LG↗

arXiv2025

Adapting to Stochastic and Adversarial Losses in Episodic MDPs with Aggregate Bandit Feedback

We study online learning in finite-horizon episodic Markov decision processes (MDPs) under the challenging aggregate bandit feedback model, where the learner observes only the cumulative loss incurred in each episode, rather than individual losses at each state-action pair. While prior work in this setting has focused exclusively on worst-case analysis, we initiate the study of best-of-both-worlds (BOBW) algorithms that achieve low regret in both stochastic and adversarial environments. We propose the first BOBW algorithms for episodic tabular MDPs with aggregate bandit feedback. In the case of known transitions, our algorithms achieve $O(\log T)$ regret in stochastic settings and ${O}(\sqrt{T})$ regret in adversarial ones. Importantly, we also establish matching lower bounds, showing the optimality of our algorithms in this setting. We further extend our approach to unknown-transition settings by incorporating confidence-based techniques. Our results rely on a combination of FTRL over occupancy measures, self-bounding techniques, and new loss estimators inspired by recent advances in online shortest path problems. Along the way, we also provide the first individual-gap-dependent lower bounds and demonstrate near-optimal BOBW algorithms for shortest path problems with bandit feedback.

cs.LG↗

arXiv2025

High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systems

In this work, we consider the problem of identifying an unknown linear dynamical system given a finite hypothesis class. In particular, we analyze the effect of the excitation input on the sample complexity of identifying the true system with high probability. To this end, we present sample complexity lower bounds that capture the choice of the selected excitation input. The sample complexity lower bound gives rise to a system theoretic condition to determine the potential benefit of experiment design. Informed by the analysis of the sample complexity lower bound, we propose a persistent excitation (PE) condition tailored to the considered setting, which we then use to establish sample complexity upper bounds. Notably, the PE condition is weaker than in the case of an infinite hypothesis class and allows analyzing different excitation inputs modularly. Crucially, the lower and upper bounds share the same dependency on key problem parameters. Finally, we leverage these insights to propose an active learning algorithm that sequentially excites the system optimally with respect to the current estimate, and provide sample complexity guarantees for the presented algorithm. Concluding simulations showcase the effectiveness of the proposed algorithm.

eess.SY↗

arXiv2025

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 $\epsilon \in (0, 1]$.

cs.LG↗

arXiv2025

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.

cs.GT↗

arXiv2025

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.

cs.RO↗

arXiv2025

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.

cs.LG↗

arXiv2024

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.

q-bio.NC↗

arXiv2024

Rethinking Data Synthesis: A Teacher Model Training Recipe with Interpretation

Recent advances in large language model (LLM) training have highlighted the need for diverse, high-quality instruction data. Recently, many works are exploring synthetic data generation using LLMs. However, they primarily focus on prompt engineering with standard supervised instruction-finetuned models, which contains a fundamental limitation: these models are optimized for general question-answering/problem-solving rather than data generation. We propose a paradigm shift named \textbf{NOMAD} by investigating how to specifically train models for data generation, demonstrating that this task differs significantly from training a classical LM. We identify two key factors: no-prompt-masked training and proper training set size selection. Our method, NOMAD, shows substantial improvements over baselines, achieving >4\% gains in TriviaQA and >2\% in GSM8K with limited training data. Finally, we offer new insights by interpreting synthetic data through the lenses of "relevance" and "novelty".

cs.CL↗

arXiv2024

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.

cs.LG↗