Adaptive designs achieve strong Neyman regret guarantees for ATE estimation.
problem Estimating unbiased average treatment effect in sequential experiments.
method Proposed adaptive designs with O ~ ( log T ) \widetilde{O}(\log T) O ( log T ) Neyman regret under boundedness assumptions and O ~ ( T ) \widetilde{O}(\sqrt{T}) O ( T ) multigroup Neyman regret in covariate-based settings. result Adaptive designs outperform non-adaptive designs in terms of Neyman regret, especially in covariate-based settings.
Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this limitation, new performance measures, including dynamic regret and adaptive regr…
We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time. Different from previous works that only utilize the convexity condition, this pa…
Online learning algorithms are designed to learn even when their input is generated by an adversary. The widely-accepted formal definition of an online algorithm's ability to learn is the game-theoretic notion of regret. We argue that the standard definition of regret becomes inadequate if the adversary is allowed to a…
New algorithm reduces control error in systems with changing dynamics.
problem Online control of systems with time-varying linear dynamics.
method Introduces adaptive regret metric and a novel meta-algorithm.
result First adaptive regret bound for online convex optimization with memory.
We propose algorithms for online principal component analysis (PCA) and variance minimization for adaptive settings. Previous literature has focused on upper bounding the static adversarial regret, whose comparator is the optimal fixed action in hindsight. However, static regret is not an appropriate metric when the un…
New online conformal prediction methods minimize strongly adaptive regret and achieve near-optimal coverage.
problem Uncertainty quantification in online settings with changing data distributions.
method Developed new online conformal prediction methods that minimize strongly adaptive regret.
result Achieve near-optimal strongly adaptive regret and approximately valid coverage.
New adaptive learning rate for FTRL reduces regret to Θ(T^2/3).
problem Minimax regret of Θ(T^2/3) in online learning.
method Adaptive learning rate framework matching stability, penalty, and bias terms.
result Improves Best-of-Both-Worlds (BOBW) regret upper bounds.
New algorithm reduces adaptive regret without projections.
problem Computational expense of projections in online convex optimization.
method Lazy gradient-based algorithm with set-membership computations.
result Near-optimal adaptive regret bounds for general convex functions.
Improved algorithm for adaptive dueling bandits with near-optimal regret bound.
problem Non-stationary dueling bandits with unknown number of preference changes.
method Elimination-based rescheduling algorithm for adaptive dynamic regret.
result Near-optimal i l d e O ( S e x t t t C W T ) ilde{O}(\sqrt{S^{ exttt{CW}} T}) i l d e O ( S e x ttt C W T ) dynamic regret bound. New algorithms reduce dynamic regret in non-stationary RL environments.
problem Optimizing policies in environments that change over time.
method POWER and POWER++ algorithms for policy optimization with dynamic regret analysis.
result POWER++ improves dynamic regret by actively adapting to non-stationarity.
Adaptive algorithms minimize regret in matching markets with contextual arm preferences.
problem Minimizing regret in matching markets with context-dependent player utilities.
method Developed adaptive algorithms for stochastic and adversarial contexts, providing upper and lower bounds.
result Achieved sublinear regret bounds for both stochastic and adversarial contexts.
New algorithm adapts to unknown demand smoothness for dynamic pricing.
problem Dynamic pricing with unknown Hölder smoothness of demand function.
method Self-similarity condition and adaptive algorithm.
result Adaptive algorithm achieves minimax optimal regret without prior knowledge of smoothness.
Study on learning strategies in adaptive Markov games with policy regret as metric.
problem Learning in dynamic Markov games with adaptive opponents is challenging.
method Introduced policy regret as a new learning metric and developed algorithms for consistent adaptive adversaries.
result Achieved T \sqrt{T} T policy regret against certain adaptive adversaries. To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms have been successfully developed to minimize the adaptive regret. However, existi…
New method achieves both universality and adaptivity in online convex optimization.
problem Achieve optimal regret guarantees without prior knowledge of function curvature.
method Introduces UniGrad, a novel approach that achieves both universality and adaptivity.
result Achieves universal regret guarantees that adapt to gradient variation.
New algorithm reduces reinforcement learning regret by adapting to interaction variability.
problem Existing reinforcement learning methods lack adaptability to interaction variability.
method Developed a variance-adaptive optimal algorithm for MNL function approximation.
result Achieved instance-wise optimal regret bounds, validating efficiency in practice.
Paper tackles online learning with interval regret, achieving adaptive bounds.
problem Non-stationary online learning over time intervals.
method Two-layer online ensemble structure with gradient variation.
result Achieves strong theoretical guarantees with adaptive bounds.
Adaptive algorithm reduces regret in causal bandits.
problem Minimize regret in causal bandits with unknown d-separators.
method Adaptive algorithm exploiting d-separators without prior knowledge.
result Significantly smaller regret than previous methods.
New algorithms improve online prediction from experts with privacy constraints.
problem Online prediction from experts under privacy constraints.
method Proposed and analyzed new algorithms for approximate and pure differential privacy.
result Achieved improved regret bounds for various adversaries.
New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.
problem Adapting to an unknown margin parameter in batched nonparametric bandits.
method Introduces the regret inflation criterion and develops RoBIN algorithm to achieve optimal regret inflation.
result The optimal regret inflation grows polynomially with the horizon T, characterized by a convex optimization problem.
Paper analyzes nonconvex bandit problems with improved adaptive methods.
problem Continuous armed bandit problems for nonconvex cost functions.
method Simple and adaptive bin splitting methods.
result Adaptive method achieves locally minimax optimal expected cumulative regret.
The paper sets bounds on how much regret is unavoidable in adaptive LQR with unknown B-matrix.
problem Understanding the limits of adaptive LQR with unknown B-matrix.
method Local asymptotic minimax regret lower bounds using van Trees' inequality and Bellman error representation.
result Logarithmic regret is impossible if the parametrization induces an uninformative optimal policy.
New algorithm reduces online learning regret in uninformed Markov games.
problem Achieving no external regret in uninformed Markov games is impossible.
method Empirical Nash-value regret, parameter-free algorithm, adaptive restart.
result Achieves O ( min { K + ( C K ) 1 / 3 , L K } ) O(\min \{\sqrt{K} + (CK)^{1/3},\sqrt{LK}\}) O ( min { K + ( C K ) 1/3 , L K }) regret bound. Adaptive linear bandit algorithm with best-of-three-worlds regret bounds.
problem Adaptive to adversarial and stochastic environments with varying sub-optimality gaps and corruption.
method Combines SCRiBLe algorithm with scaled-up sampling and optimistic online learning.
result Achieves best-of-three-worlds regret bounds of O ( T log T ) O(\sqrt{T \log T}) O ( T log T ) for adversarial and O ( log T Δ min + C log T Δ min ) O(\frac{\log T}{Δ_{\min}} + \sqrt{\frac{C \log T}{Δ_{\min}}}) O ( Δ m i n l o g T + Δ m i n C l o g T ) for stochastic environments. TSAC achieves optimal frequentist regret in adaptive control of LQRs.
problem Adaptive control of stabilizable linear-quadratic regulators with unknown dynamics.
method Thompson Sampling (TS) for adaptive control of LQRs, with a novel early exploration strategy.
result Achieves i l d e O ( T ) ilde O(\sqrt{T}) i l d e O ( T ) regret, optimal for multidimensional systems. Optimistic covariance-adaptive algorithms improve combinatorial semi-bandits regret.
problem Optimal regret in stochastic combinatorial semi-bandits with adaptive covariance estimation.
method Design of OLS-UCB-C and COS-V algorithms leveraging online covariance estimation.
result Improved gap-free regret with T^1/2 complexity for COS-V.
We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high…
Optimal switching regret for all segmentations in online convex optimisation.
problem Non-stationary online convex optimisation problems.
method Developed an efficient algorithm to achieve optimal switching regret on every possible segmentation.
result Achieved asymptotically optimal switching regret on every possible segmentation simultaneously.
Efficient RL algorithms for linear function approximation with limited adaptivity constraints.
problem Limited adaptivity in reinforcement learning with linear function approximation.
method Proposed two efficient online RL algorithms for episodic linear Markov decision processes under batch learning and rare policy switch models.
result Achieved efficient regret bounds for both batch learning and rare policy switch models, with substantial reduction in adaptivity.
New algorithms reduce regret for convex bandits with small comparator norms.
problem Optimizing in bandit convex optimization with varying comparator norms.
method Developed algorithms using techniques from full-information setting and new gradient estimators.
result Regret bounds are small when comparator norm is small.
Adaptive clustering and personalization algorithms minimize regret in multi-agent stochastic linear bandits.
problem Minimizing regret in a multi-agent stochastic linear bandits framework with user heterogeneity.
method Proposes a novel algorithm that refines cluster identities and minimizes regret, adapting to cluster separation and user parameter deviations.
result Regret scales as O ( T / N ) \mathcal{O}(\sqrt{T/N}) O ( T / N ) for well-separated clusters and O ( T 1 2 + ε / ( N ) 1 2 − ε ) \mathcal{O}(T^{\frac{1}{2} + \varepsilon}/(N)^{\frac{1}{2} -\varepsilon}) O ( T 2 1 + ε / ( N ) 2 1 − ε ) for poorly separated clusters. New algorithms avoid a dominant lower-order term in heavy-tailed loss settings.
problem Prediction with heavy-tailed losses without prior knowledge.
method Adaptive algorithms that avoid the maximum of losses as a lower-order term in regret.
result Improved regret bounds of O ( θ T log ( K ) ) \mathcal{O}(\sqrt{θT\log(K)}) O ( θ T log ( K ) ) and O ( θ log ( K T ) / Δ min ) \mathcal{O}(θ\log(KT)/Δ_{\min}) O ( θ log ( K T ) / Δ m i n ) . RAVEN-UCB addresses non-stationary MAB problems with tighter regret bounds.
problem Non-stationary environments in multi-armed bandits.
method Combines variance-aware adaptation with three innovations: confidence bounds, adaptive control, and recursive updates.
result Achieves tighter regret bounds than UCB1 and UCB-V.
Unified algorithm for optimizing rewards in stochastic path problems.
problem Optimizing rewards in stochastic path problems with unknown reward scales.
method A simple optimistic algorithm with regret guarantees.
result Regret bound matches best known results for SSP with all non-positive rewards.
We develop a new theoretical framework, the \emph{envelope complexity}, to analyze the minimax regret with logarithmic loss functions and derive a Bayesian predictor that adaptively achieves the minimax regret over high-dimensional ℓ 1 \ell_1 ℓ 1 -balls within a factor of two. The prior is newly derived for achieving the mini…
AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.
problem Adaptive control in partially observable linear dynamical systems.
method AdaptOn algorithm that estimates system dynamics through online learning and gradient descent.
result AdaptOn achieves a logarithmic regret bound of polylog(T) after T steps.
New algorithm reduces regret for kernelized bandits by adapting to specific problem instances.
problem Efficiently learning the optimizer of an unknown function in RKHS with noisy oracle.
method Instance-dependent regret analysis and a new minimax near-optimal algorithm.
result New algorithm achieves better performance on specific problem instances.
We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and "hard" problems. For easy problems, it additionally achieves logarithmic individual…
New algorithm reduces dynamic regret by adapting to comparator complexity.
problem Nonstationary sequential decision making with unbounded domains.
method Sparse coding framework to adapt to comparator complexity.
result Improves dynamic regret bounds by adapting to comparator energy and sparsity.
Mirror descent with an entropic regularizer is known to achieve shifting regret bounds that are logarithmic in the dimension. This is done using either a carefully designed projection or by a weight sharing technique. Via a novel unified analysis, we show that these two approaches deliver essentially equivalent bounds …
New algorithm reduces dynamic regret in time-varying movement costs.
problem Dynamic regret in online convex optimization with time-varying movement costs.
method Introduced a novel algorithm for time-varying movement costs, achieving comparator-adaptive dynamic regret bound.
result Established first comparator-adaptive dynamic regret bound of O ~ ( ( M 2 + M P T ) ( T + ∑ t λ t ) ) \widetilde{\mathcal{O}}(\sqrt{(M^2+MP_T)(T+\sum_t λ_t)}) O ( ( M 2 + M P T ) ( T + ∑ t λ t ) ) . UCB algorithms improve on bandit problems with precise regret analysis and adaptive inference.
problem Understanding the performance and statistical inference of UCB algorithms in multi-armed bandit problems.
method Deterministic characterization of arm pulls and precise regret analysis.
result UCB algorithms' maximal regret deviates from minimax regret by a logarithmic factor, and the Lai-Robbins formula is exact only under specific conditions.
Algorithm adapts to shifting domains with minimal label queries.
problem Adaptive learning in online machine learning systems with domain shifts.
method Adaptive algorithm balancing regret and label queries for hidden domains.
result Achieves lower regret compared to uniform and greedy queries.
New algorithm reduces regret for linear bandits with unknown noise variance.
problem Finding optimal actions in linear bandits with varying noise variance.
method Adaptive algorithm with Freedman-type concentration inequality and multi-layer structure.
result Achieves i l d e O ( d ∑ k = 1 K σ k 2 + d ) ilde{O}(d \sqrt{\sum_{k = 1}^K σ_k^2} + d) i l d e O ( d ∑ k = 1 K σ k 2 + d ) regret for linear bandits. Significant improvements in regret analysis for adaptive online learning problems.
problem Exploiting low variance in online learning problems without known variances.
method Novel peeling-based regret analysis leveraging elliptical potential `count` lemma.
result Significant improvements in regret bounds for linear bandits and linear mixture MDPs.
Unified framework for analyzing online convex optimization across various settings.
problem Analyzing online convex optimization in different settings and feedback types.
method Unified framework allowing systematic proposal and analysis of meta-algorithms.
result Comparable regret bounds for various feedback types and adversary types.
Paper tackles domain adaptation for contextual bandits with sub-linear regret.
problem Adapting contextual bandit algorithms across domains with distribution shift.
method Learn a bandit model for the target domain using feedback from the source domain.
result Sub-linear regret bound maintained across domains.