The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
Study optimizes dynamic product selection and pricing using censored preference feedback.
problem Maximizing revenue from dynamic assortment and pricing decisions.
method Proposes a censored multinomial logit model and LCB pricing strategy combined with UCB or TS product selection.
result Achieves optimal regret bounds for dynamic pricing and selection.
Upper and lower bounds on regret for noisy optimization of Brownian motion.
problem Optimizing a one-dimensional Brownian motion with noisy observations.
method Upper bound uses confidence bounds and Markov property; lower bound uses hypothesis testing reduction.
result Upper and lower bounds are tight up to a factor of O ( ( log T ) 1.5 ) O((\log T)^{1.5}) O (( log T ) 1.5 ) . A bandit problem with filtered Poisson process data.
problem Maximizing points revealed from a continuum action space.
method Upper confidence bound algorithm with data-adaptive discretisation.
result Regret bound of O(T^(2/3)) under Lipschitz assumption.
New bounds for Bayesian bandits show prior improves performance.
problem Improving regret bounds for Bayesian bandits.
method Upper confidence bound algorithm with finite-time logarithmic regret bounds.
result Derives O ( c Δ log n ) O(c_Δ\log n) O ( c Δ log n ) and O ( c h log 2 n ) O(c_h \log^2 n) O ( c h log 2 n ) upper bounds for Bayesian bandits. A new algorithm for better decision-making in recommendation systems.
problem Stochastic multi-armed bandit problem and cold start problem in recommender systems.
method Proposes Hellinger-UCB, a variant of UCB algorithm using squared Hellinger distance.
result Hellinger-UCB reaches the theoretical lower bound and outperforms other algorithms in practical applications.
This paper is devoted to regret lower bounds in the classical model of stochastic multi-armed bandit. A well-known result of Lai and Robbins, which has then been extended by Burnetas and Katehakis, has established the presence of a logarithmic bound for all consistent policies. We relax the notion of consistence, and e…
BILBO optimizes bilevel problems without repeated lower-level optimizations.
problem Challenges in bilevel optimization, especially in noisy, constrained, and derivative-free settings.
method BILevel Bayesian Optimization (BILBO) that optimizes both levels simultaneously, using confidence-bounds and function query selection.
result Theoretical and empirical evidence of BILBO's effectiveness on various problems.
New algorithm optimizes online decision-making with dynamically generated actions.
problem Balancing action generation costs with optimal decision-making in online learning.
method Doubly-optimistic algorithm using LCB for action selection and UCB for action generation.
result Achieves optimal regret bound of O ( T d d + 2 d d d + 2 + d T log T ) O(T^{\frac{d}{d+2}}d^{\frac{d}{d+2}} + d\sqrt{T\log T}) O ( T d + 2 d d d + 2 d + d T log T ) . Algorithm aggregates rewards from multiple players to learn related tasks in online bandit learning.
problem Learning related but slightly different tasks in an online setting with heterogeneous feedback.
method RobustAgg ( ε ) (ε) ( ε ) algorithm that aggregates rewards from different players. result Achieves instance-dependent regret guarantees and nearly matching lower bounds.
New algorithms tackle latent bandit problems with lower regret.
problem Learning optimal actions in a latent state setting.
method General algorithms based on UCBs and Thompson sampling, aware of model uncertainty.
result Our methods have lower regret than classic bandit policies when latent states are fewer than actions.
Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in many applications where rewards are binary. However, most theoretical analyses …
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on 1 / δ 1/δ 1/ δ with probability δ δ δ . A new federated multi-armed bandit framework with personalization balances generalization and personalization.
problem Balancing generalization and personalization in federated multi-armed bandits.
method Proposed a Personalized Federated Upper Confidence Bound (PF-UCB) algorithm to achieve a O ( log ( T ) ) O(\log(T)) O ( log ( T )) regret. result PF-UCB achieves an O ( log ( T ) ) O(\log(T)) O ( log ( T )) regret regardless of personalization degree and has similar instance dependency to lower bound. A new differentiable UCB algorithm for linear bandits learns adaptive confidence bounds.
problem Inability of UCB to strike optimal exploration-exploitation due to confidence bounds.
method Proposes a differentiable linear bandit algorithm and a gradient estimator for learning adaptive confidence bounds.
result Achieves a i l d e O ( β ^ d T ) ilde{\mathcal{O}}(\hatβ\sqrt{dT}) i l d e O ( β ^ d T ) upper bound of T T T -round regret. Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.
problem Minimizing regret in Gaussian process bandit optimization.
method Gaussian process upper confidence bound (GP-UCB) algorithm with refined analysis.
result Achieves O ( T ln 2 T ) O(\sqrt{T \ln^2 T}) O ( T ln 2 T ) cumulative regret under squared exponential kernel. This note gives a short, self-contained, proof of a sharp connection between Gittins indices and Bayesian upper confidence bound algorithms. I consider a Gaussian multi-armed bandit problem with discount factor γ γ γ . The Gittins index of an arm is shown to equal the γ γ γ -quantile of the posterior distribution of the arm'…
Bayes-UCBVI tackles reinforcement learning with a new upper confidence bound method.
problem Optimizing exploration in reinforcement learning without bonuses.
method Bayes-UCBVI uses a quantile of a Q-value function posterior as an upper confidence bound.
result Proves a regret bound of order O ~ ( H 3 S A T ) \widetilde{O}(\sqrt{H^3SAT}) O ( H 3 S A T ) for tabular reinforcement learning. Improved Bayesian optimisation method using randomised Gaussian process UCB.
problem Improving performance in Bayesian optimisation.
method Developed a modified Gaussian process upper confidence bound (GP-UCB) acquisition function.
result The method achieves better performance than GP-UCB in various problems.
The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the…
One-bit feedback suffices for a bandit problem's optimal strategy.
problem Optimal strategy for multi-armed bandit problem with limited feedback.
method Coding and decoding schemes for one-bit feedback to mimic full-reward feedback.
result Regret ratio approaches 1 with one-bit feedback.
Bayesian methods improve drug discovery experiment design.
problem Optimizing drug screening experiments in high-dimensional data.
method Bayesian inference and optimisation with upper confidence bound algorithms, Thompson sampling, and sparse tree search.
result Sparse tree search techniques outperform other methods in drug toxicity screening.
A new method optimizes robustness measures under input uncertainty using randomized Gaussian process upper confidence bound.
problem Optimizing robustness measures under input uncertainty.
method Randomized robustness measure GP-UCB (RRGP-UCB) that samples β from a chi-squared-based distribution.
result RRGP-UCB provides tight bounds on expected regret.
New algorithm minimizes Bayesian regret in offline linear bandits.
problem Minimizing Bayesian regret in offline linear bandits.
method Proposes a new algorithm that directly minimizes upper bounds on Bayesian regret using conic optimization.
result Upper bounds are tight and guarantee superior performance compared to LCB.
We study an original problem of pure exploration in a strategic bandit model motivated by Monte Carlo Tree Search. It consists in identifying the best action in a game, when the player may sample random outcomes of sequentially chosen pairs of actions. We propose two strategies for the fixed-confidence setting: Maximin…
Optimal strategy for reinforcement learning with delayed observations.
problem Delayed state observation in reinforcement learning.
method Combines augmentation method and upper confidence bound approach.
result Minimax optimal regret bound of i l d e O ( H D max S A K ) ilde{\mathcal{O}}(H \sqrt{D_{\max} SAK}) i l d e O ( H D m a x S A K ) . GP-UCB performs suboptimally under certain conditions, as shown by a new regret lower bound.
problem The suboptimality of GP-UCB under polynomial effective optimism.
method Analysis of effective optimism level and new regret lower bound.
result GP-UCB is not minimax optimal under polynomial growth of effective optimism.
Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration inequalities, which thus lead to over-exploration. In this paper, we propose a n…
In this paper, the method UCB-RS, which resorts to recommendation system (RS) for enhancing the upper-confidence bound algorithm UCB, is presented. The proposed method is used for dealing with non-stationary and large-state spaces multi-armed bandit problems. The proposed method has been targeted to the problem of the …
New method shows multi-objective bandits are not harder than single-objective ones.
problem Comparing multi-objective bandits to single-objective ones.
method Upper and lower confidence-bound estimators for every arm-objective pair, using top-two races and uncertainty-greedy rule.
result Achieves Pareto regret of \(O(
icefrac{\log T}{g^\dagger})\), matching lower bound of \(Ω(
icefrac{\log T}{g^\dagger})\).
New principle optimizes bandit decisions with context.
problem Dealing with general function classes and large context spaces in bandits.
method Upper Counterfactual Confidence Bounds (UCCB) principle.
result Proves optimality and efficiency in complex settings.
The paper proposes a novel upper confidence bound (UCB) procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples. The procedure cannot be improved in the sense that the number of samples required to identify the best arm i…
TS-UCB improves Thompson Sampling with minimal extra computation.
problem Online decision problems with bandit feedback.
method TS-UCB uses posterior samples and upper confidence bounds to select arms.
result TS-UCB achieves lower regret on various datasets.
New algorithms prove self-play can be effective in competitive RL.
problem Proving self-play algorithms' effectiveness in competitive reinforcement learning.
method Introduced Value Iteration with Upper/Lower Confidence Bound (VI-ULCB) and explore-then-exploit algorithms.
result Achieved regret bounds of i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) and i l d e O ( T 2 / 3 ) ilde{\mathcal{O}}(T^{2/3}) i l d e O ( T 2/3 ) . The paper optimizes risk-sensitive RL with CVaR, achieving near-minimax-optimal results.
problem Optimizing risk-sensitive reinforcement learning with CVaR objective.
method Developed algorithms for multi-arm bandits and online RL in MDPs, achieving near-minimax-optimal regret.
result Achieved near-minimax-optimal regret of O ( τ − 1 S A K ) O(τ^{-1}\sqrt{SAK}) O ( τ − 1 S A K ) for constant τ τ τ . New model improves website ranking by considering user choices as a whole.
problem Optimizing content ordering for user clicks in website design.
method Introduced multinomial logit (MNL) choice model to LTR framework, proposing UCB algorithms.
result Proved theoretical bounds on regret for UCB algorithms in both known and unknown position parameter settings.
A new online learning problem, CAB, tackles matching platforms to maximize user satisfaction.
problem Maximizing matches in a matching platform can lead to dissatisfaction and churn.
method Developed CAB, an online learning problem that maximizes arm satisfaction, and analyzed algorithms like UCB and Thompson sampling.
result CAB-UCB achieves higher cumulative satisfaction than baselines in experiments.
UCB algorithm provides stable sample means for sequential data.
problem Challenges in inferential tasks with sequential data.
method Stability property of UCB algorithm for multiarmed bandit problems.
result UCB algorithm ensures asymptotically normal sample means.
This paper improves GP-UCB by using a shifted exponential distribution for confidence parameters.
problem Theoretical confidence parameter in GP-UCB increases with iterations, leading to large values.
method Introduced IRGP-UCB, a randomized variant of GP-UCB using a shifted exponential distribution for confidence parameters.
result IRGP-UCB achieves sub-linear regret without increasing the confidence parameter.
UCBMQ improves Q-learning by adding momentum to correct bias and limit regret.
problem Improving Q-learning's bias and regret in reinforcement learning.
method UCBMQ combines Q-learning with an upper confidence bound and momentum term.
result UCBMQ guarantees a regret of O ( H 3 S A T + H 4 S A ) O(\sqrt{H^3SAT}+ H^4 S A ) O ( H 3 S A T + H 4 S A ) with a linear second-order term in S S S . Paper proposes a new UCB approach for estimating maximum mean.
problem Estimating the maximum mean in various applications.
method Upper Confidence Bound (UCB) approach with adaptive sampling.
result LSA estimator shows faster bias decay compared to GA.
Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.
problem Theoretical justification for Bayesian bandit algorithms with approximate inference in stochastic linear bandits.
method Proposed a theoretical framework to analyze approximate inference impact and conducted frequentist regret analysis on LinTS and LinBUCB.
result LinTS and LinBUCB preserve their original regret upper bounds with larger constant terms in approximate inference settings.
Proposes a method to compute valid lower confidence bounds for multiple models selected based on their performance.
problem Model selection and evaluation in machine learning.
method Interprets model selection as a simultaneous inference problem, uses bootstrap tilting and maxT-type multiplicity correction.
result Yields valid lower confidence bounds that are at least as good as standard approaches and reliably reach nominal coverage probability.
This paper proposes a DGP approach with UCBs for point target tracking over WSNs.
problem Uncertainty quantification in distributed machine learning-based tracking over WSNs.
method Distributed Gaussian process (DGP) approach with upper confidence bounds (UCBs).
result UCBs provide 88% and 42% higher probability of encompassing true target states in X and Y coordinates, respectively.
Study contextual bandits with stage-wise constraints, proving regret bounds and extending results.
problem Contextual bandits with stage-wise constraints in high probability and expectation settings.
method Upper-confidence bound algorithms for linear and non-linear reward/cost functions, extending to multiple constraints.
result Regret bounds for various settings, including non-linear reward/cost functions.
Improved UCB method for stochastic bandits using distance tuning.
problem Improving performance in stochastic bandit problems.
method Tuning confidence bounds based on bandit distance.
result Empirically shows increased performance compared to existing methods.
We present two algorithms for Bayesian optimization in the batch feedback setting, based on Gaussian process upper confidence bound and Thompson sampling approaches, along with frequentist regret guarantees and numerical results.
We consider the dynamic assortment optimization problem under the multinomial logit model (MNL) with unknown utility parameters. The main question investigated in this paper is model mis-specification under the ε \varepsilon ε -contamination model, which is a fundamental model in robust statistics and machine learning. In…