14 accepted papers
Training data reconstruction from KKT conditions has shown striking empirical success, yet it remains unclear when the resulting KKT equations have unique solutions and, even in identifiable regimes, how to reliably recover solutions by optimization. This work hereby focuses on these two complementa…
Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent missing data issue echoes the multi-marginal optimal transpo…
We study the evolution of information in interactive decision making through the lens of a stochastic multi-armed bandit problem. Focusing on a fundamental example where a unique optimal arm outperforms the rest by a fixed margin, we characterize the optimal success probability and mutual informatio…
Real-time and high-performance 3D object detection plays a critical role in autonomous driving and robotics. Recent pillar-based 3D object detectors have gained significant attention due to their compact representation and low computational overhead, making them suitable for onboard deployment and q…
We develop a unifying framework for information-theoretic lower bound in statistical estimation and interactive decision making. Classical lower bound techniques---such as Fano's method, Le Cam's method, and Assouad's lemma---are central to the study of minimax risk in statistical estimation, yet ar…
We consider realizable contextual bandits with general function approximation, investigating how small reward variance can lead to better-than-minimax regret bounds. Unlike in minimax regret bounds, we show that the eluder dimension $d_{\text{elu}}$$-$a measure of the complexity of the function cl…
Motivated by the recent discovery of a statistical and computational reduction from contextual bandits to offline regression \citep{simchi2020bypassing}, we address the general (stochastic) Contextual Markov Decision Process (CMDP) problem with horizon $H$ (as known as CMDP with $H$ layers). In this…
The classical theory of statistical estimation aims to estimate a parameter of interest under data generated from a fixed design (''offline estimation''), while the contemporary theory of online learning provides algorithms for estimation under adaptively chosen covariates (''online estimation''). M…
We propose a generalization of the classical G-optimal design concept to non-linear function classes. The criterion, termed F -design, coincides with G-design in the linear case. We compute the value of the optimal design, termed the F-condition number, for several non-linear function classes. We fu…
Classical analysis of convex and non-convex optimization methods often requires the Lipschitz continuity of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness condition with the Hessian norm bounded by an affi…
We consider the problem of interactive decision making, encompassing structured bandits and reinforcement learning with general function approximation. Recently, Foster et al. (2021) introduced the Decision-Estimation Coefficient, a measure of statistical complexity that lower bounds the optimal reg…
We study minimax optimal reinforcement learning in episodic factored Markov decision processes (FMDPs), which are MDPs with conditionally independent transition components. Assuming the factorization is known, we propose two model-based algorithms. The first one achieves minimax optimal regret guara…
The exploration bonus is an effective approach to manage the exploration-exploitation trade-off in Markov Decision Processes (MDPs). While it has been analyzed in infinite-horizon discounted and finite-horizon problems, we focus on designing and analysing the exploration bonus in the more challengin…
Importance sampling (IS) is a common reweighting strategy for off-policy prediction in reinforcement learning. While it is consistent and unbiased, it can result in high variance updates to the weights for the value function. In this work, we explore a resampling strategy as an alternative to rewei…