New algorithm optimizes smooth functions with Hölder exponent > 1.
problem Optimizing smooth functions with unknown Hölder exponent > 1.
method Two-layer algorithms using misspecified linear/polynomial bandit algorithms in bins.
result Regret bound of O ~ ( T d + α d + 2 α ) \tilde{O}(T^{\frac{d+\alpha}{d+2\alpha}}) O ~ ( T d + 2 α d + α ) for α > 1 \alpha > 1 α > 1 . We study a nonparametric contextual bandit problem where the expected reward functions belong to a Hölder class with smoothness parameter β β β . We show how this interpolates between two extremes that were previously studied in isolation: non-differentiable bandits ( β ≤ 1 β\leq1 β ≤ 1 ), where rate-optimal regret is achieved by run…
Randomized exploration in linear bandits achieves optimal regret bounds.
problem Optimizing exploration in high-dimensional linear bandit problems.
method Analysis of Thompson sampling without forced optimism.
result Randomized exploration algorithms achieve an O ( d n log ( n ) ) O(d\sqrt{n} \log(n)) O ( d n log ( n )) regret bound in smooth, strongly convex action spaces. This paper studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
problem Optimizing an unknown function with limited evaluations.
method Studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
result Minimax rates over Besov spaces are identical to those over the smallest Hölder space into which Besov spaces embed.
Investigates sequential problems on graph structures and large action spaces.
problem Sequential decision-making on graph structures and large action spaces.
method Spectral bandits, side observations, influence maximization, kernel bandits, polymatroid bandits, function optimization, infinitely many-arms bandits.
result Contributions to graph and structured bandits.
Paper tackles efficient BAI in graph-smooth bandits.
problem Best arm identification with graph smoothness constraint.
method Gradient ascent algorithm for sample complexity.
result Asymptotically optimal strategy for BAI.
Efficient algorithms for contextual bandits with smooth regret in continuous action spaces.
problem Efficient learning in large or continuous action spaces.
method Smooth regret notion and efficient algorithms for general function approximation.
result Statistically and computationally efficient algorithms for contextual bandits with smooth regret.
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.
New algorithm controls linear systems with bandit feedback, achieving optimal regret.
problem Controlling linear systems with bandit feedback under adversarial costs.
method Developed a new algorithm for linear control with memory optimization technique.
result Achieved optimal regret growth proportional to square root of time horizon.
The paper tackles minimax optimality in continuum contextual bandits with Hölder continuity.
problem Minimizing regret in a continuum of contexts with Hölder continuity.
method Proves a static-to-contextual regret conversion theorem and analyzes various dependency cases.
result Achieves minimax optimal contextual regret for convex and strongly convex bandits.
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.
Study on selecting between base algorithms in stochastic bandit problems.
problem Model selection in stochastic environments with contextual information.
method Developed a meta-algorithm-base algorithm abstraction with a smoothing transformation for optimal O ( T ) O(\sqrt{T}) O ( T ) guarantees. result Optimal O ( T ) O(\sqrt{T}) O ( T ) model selection guarantees for stochastic contextual bandit problems. The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem based on a cost function over a continuous space. We propose a stochastic mirror descent algorithm and …
Study nonparametric contextual bandits with batched updates, achieving optimal regret.
problem Optimal regret in nonparametric contextual bandits with batch constraints.
method Dynamic binning of covariate space, optimal regret achieved.
result Achieves optimal regret (up to logarithmic factors) for nonparametric contextual bandits.
Greedy algorithm nearly outperforms exploration in contextual bandits.
problem Balancing exploration and exploitation in online learning.
method Smoothed analysis of the greedy algorithm in linear contextual bandits.
result Greedy algorithm nearly matches Bayesian regret rate under diversity conditions, with regret at most O ( T 1 / 3 ) O(T^{1/3}) O ( T 1/3 ) . This paper optimizes attacks on stochastic bandits and proposes defenses against them.
problem Optimizing adversarial attacks on stochastic bandit algorithms.
method Designs optimal attack strategies and proposes defense algorithms.
result Optimal attack strategies and defense algorithms achieve near perfect performance.
We study contextual bandit learning with an abstract policy class and continuous action space. We obtain two qualitatively different regret bounds: one competes with a smoothed version of the policy class under no continuity assumptions, while the other requires standard Lipschitz assumptions. Both bounds exhibit data-…
In this paper we consider the problem of online stochastic optimization of a locally smooth function under bandit feedback. We introduce the high-confidence tree (HCT) algorithm, a novel any-time X \mathcal{X} X -armed bandit algorithm, and derive regret bounds matching the performance of existing state-of-the-art in term…
Paper addresses privacy in combinatorial semi-bandits with improved bounds.
problem Privacy-preserving learning in combinatorial semi-bandits with additional dimension dependence.
method Proposes novel algorithms and proves optimal regret bounds for LDP and DP settings.
result Achieves nearly optimal regret bounds for LDP and DP settings, matching non-private rates.
The paper tackles a bandit problem on graphs with smooth functions, aiming to recommend items with high expected ratings.
problem Online learning problems involving graphs, such as content-based recommendation.
method Introduced the notion of effective dimension and proposed two algorithms for solving the problem.
result The algorithms can learn good estimators of user preferences from just tens of nodes evaluations.
OE2D framework reduces contextual bandits to offline regression for near-optimal regret.
problem Efficiently learning contextual bandits with large action spaces and complex reward functions.
method Offline Estimation to Decisions (OE2D) algorithm that reduces contextual bandits to offline regression.
result Near-optimal regret for contextual bandits with large action spaces and O ( log T ) O(\log T) O ( log T ) calls to an offline regression oracle. Unified analysis of kernel-based and locally adaptive bandit optimization methods.
problem Performance of bandit optimization algorithms in RKHS functions.
method Investigates the relationship between kernel regularity and algorithmic performance, characterizing spectral properties of various kernels.
result Unified framework for analyzing kernel-based and locally adaptive bandit algorithms, deriving explicit regret bounds.
We consider the closely related problems of bandit convex optimization with two-point feedback, and zero-order stochastic convex optimization with two function evaluations per round. We provide a simple algorithm and analysis which is optimal for convex Lipschitz functions. This improves on \cite{dujww13}, which only p…
Adaptive smooth non-stationary bandits achieve optimal regret rates without knowing parameters.
problem Smooth non-stationary bandits with Hölder class rewards.
method Established optimal dynamic regret rate and adaptive algorithm.
result Optimal dynamic regret can be attained adaptively without knowing Hölder exponent and coefficient.
New algorithm optimizes functions in Matérn kernel RKHS with noisy feedback.
problem Optimizing functions in RKHS of Matérn kernel with noisy bandit feedback.
method π-GP-UCB algorithm with guaranteed sublinear regret for all ν > 1 and d ≥ 1.
result First practical approach with guaranteed sublinear regret for all ν > 1 and d ≥ 1.
New algorithm tackles smooth online learning with optimal regret.
problem Smoothed online learning with adversarial distributions.
method Oracle-efficient algorithms for nonparametric function classes.
result Oracle-efficient algorithms achieve optimal regret bounds.
Saddle-point optimization problems are an important class of optimization problems with applications to game theory, multi-agent reinforcement learning and machine learning. A majority of the rich literature available for saddle-point optimization has focused on the offline setting. In this paper, we study nonstationar…
New algorithm reduces regret in bandit optimization for high-dimensional data.
problem Optimizing decisions in uncertain environments with high-dimensional data.
method Inspired by online Newton step, proposes a simple and efficient BCO algorithm.
result Achieves optimal regret bounds for κ κ κ -convex functions. Improved online learning for hidden-convex losses achieves optimal regret.
problem Adversarial online learning with nonconvex losses that become convex after reparameterization.
method Algorithmic equivalence between OGD and OMD on convex losses, with Hessian compatibility condition.
result OGD achieves O ( T ) \mathcal{O}(\sqrt{T}) O ( T ) regret for hidden-convex losses, matching optimal rate. Algorithm tackles adaptive discretization in adversarial Lipschitz bandits for dynamic pricing and auctions.
problem Adaptive discretization in adversarial Lipschitz bandits.
method Adversarial Zooming algorithm for adaptive discretization.
result First algorithm for adversarial Lipschitz bandits with instance-dependent regret bounds.
We study a non-parametric multi-armed bandit problem with stochastic covariates, where a key complexity driver is the smoothness of payoff functions with respect to covariates. Previous studies have focused on deriving minimax-optimal algorithms in cases where it is a priori known how smooth the payoff functions are. I…
Improved control approach for correlated bandits with better performance.
problem General multi-armed bandit problem with correlated elements.
method Introducing entropy regularisation to obtain a smooth asymptotic approximation of the value function, leading to a semi-index approximation of the optimal decision process.
result Performance of Asymptotic Randomised Control (ARC) algorithm compares favorably with other approaches.
We define a novel family of algorithms for the adversarial multi-armed bandit problem, and provide a simple analysis technique based on convex smoothing. We prove two main results. First, we show that regularization via the \emph{Tsallis entropy}, which includes EXP3 as a special case, achieves the Θ ( T N ) Θ(\sqrt{TN}) Θ ( T N ) minim…
New algorithm reduces neural net error in contextual bandits.
problem Neural contextual bandits with general activation functions.
method Proposed an efficient algorithm with sublinear regret bound.
result Demonstrated provably sublinear regret bound in finite regime.
This paper tackles fair online decision-making in contextual bandits, achieving optimal performance and fairness.
problem Fairness in online decision-making systems under strategic manipulation.
method Develops algorithms for linear and smooth reward functions, maintaining fairness and optimal regret.
result Achieves nearly minimax-optimal regret with strong fairness guarantees, even in the presence of attacks.
Unified meta-algorithm improves average performance across similar tasks in adversarial bandits.
problem Improving performance across multiple similar tasks in adversarial bandit settings.
method Unified meta-algorithm for multi-armed bandits and bandit linear optimization, tuning initialization, step-size, and entropy parameters.
result Unified meta-algorithm yields setting-specific guarantees for MAB and BLO, improving task-averaged regret.
The paper analyzes the sliding regret of stochastic bandit algorithms.
problem Measuring the one-shot behavior of no-regret algorithms in stochastic bandits.
method Introducing sliding regret to measure the worst pseudo-regret over a time-window.
result Randomized methods have optimal sliding regret, while index policies have the worst possible sliding regret.
New algorithm reduces regret for many bandit algorithms with logarithmic dependence on number of algorithms.
problem Combining and learning over a large set of adversarial bandit algorithms to track the best one.
method Proposes a new algorithm (CORRAL) with logarithmic regret dependence on the number of base algorithms.
result Achieves optimal switching regret for adversarial linear bandits over a d d d -dimensional ℓ p \ell_p ℓ p unit-ball. New lower bounds for combinatorial multi-armed bandits for general reward functions.
problem Maximizing reward in sequential decisions with sets of arms.
method Proved tight regret lower bounds for all smooth reward functions under mild assumptions.
result Lower bounds are tight up to log-factors for monotone reward functions.
Framework reduces contextual bandit learning to offline regression with near-optimal regret.
problem Efficient learning with large action spaces and complex reward functions.
method Offline Estimation to Decisions (OE2D) algorithm that minimizes regret with near-optimal oracle calls.
result Near-optimal regret for contextual bandits with large action spaces and O ( l o g ( T ) ) O(log(T)) O ( l o g ( T )) offline oracle calls. We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side inf…
Bandit problem on graphs aims to recommend items with high expected ratings.
problem Online learning problems involving graphs, such as content-based recommendation.
method Study of a bandit problem on graphs, introducing effective dimension and proposing algorithms.
result Proposed algorithms scale linearly and sublinearly in the effective dimension, improving cumulative regret.
In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{ö}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli an…
Improved regret bounds for structured linear contextual bandits with Gaussian noise.
problem Optimizing bandit learning algorithms for structured contexts with Gaussian perturbations.
method Proposed simple greedy algorithms for structured linear contextual bandits with Gaussian noise.
result Unified regret analysis for structured parameters with geometric quantities as bounds.
VOGP efficiently identifies Pareto optimal solutions in black-box vector optimization.
problem Black-box vector optimization with incomplete order relations.
method VOGP is an adaptive elimination algorithm using Gaussian process bandits.
result VOGP achieves theoretical guarantees with sample complexity bounds.
Optimal strategy proposed for maximizing cumulative reward in continuum-armed bandits.
problem Maximizing cumulative reward in a scenario with limited resources and unknown stochastic rewards.
method Proposed an optimal strategy for a nonparametric setting with side information on actions.
result Optimal regret scales as \(O(T^{1/3})\) up to poly-logarithmic factors when \(T\) is proportional to \(N\).
Paper tackles transfer learning for contextual multi-armed bandits under covariate shift.
problem Nonparametric contextual multi-armed bandits with covariate shift.
method Established minimax rate of convergence, proposed transfer learning algorithm.
result Achieved near-optimal statistical guarantees for learning in target domain.
Study bandit problem on smooth graph functions for recommender systems.
problem Online learning problems involving graphs, like content-based recommendation.
method Introduced spectral bandit problem and two algorithms that scale linearly in effective dimension.
result Learned user preferences for thousands of items from just tens nodes evaluations.