Paper solves stochastic contextual linear bandits using linear bandit algorithms.
problem Stochastic contextual linear bandits with unknown context distribution.
method Establishes a reduction framework to convert to linear bandit problems.
result Achieves nearly optimal regret bound of O ( d T log T ) O(d\sqrt{T\log T}) O ( d T log T ) . Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.
problem Identifying the best arm in stochastic linear bandits with fixed confidence.
method Extending an algorithm designed for Best Arm Identification to the ε ε ε -Thresholding Bandit Problem (TBP). result Asymptotically optimal algorithm for TBP.
A meta-UCB method combines stochastic bandit algorithms.
problem Combining multiple stochastic bandit algorithms efficiently.
method Meta-UCB procedure solving an N-armed bandit problem.
result Final regret depends only on the best base algorithm's regret.
Improved algorithms for stochastic linear bandits using tighter confidence sequences.
problem Stochastic linear bandits with improved worst-case regret guarantees.
method Novel tail bound for adaptive martingale mixtures to construct tighter confidence sequences.
result Linear bandit algorithm achieves competitive worst-case regret.
New algorithm reduces regret from sqrt(T) to polylog(T) in stochastic contextual linear bandits.
problem Achieving logarithmic regret in stochastic contextual linear bandits.
method Low Regret Stochastic Contextual Bandits ( exttt{LR-SCB}) algorithm, exploiting stochastic contexts and parameter estimation.
result Logarithmic regret (polylog(T)) achieved, improving over sqrt(T) lower bound.
New algorithm reduces regret in stochastic bandit convex optimization.
problem Optimizing decisions in uncertain environments with convex losses.
method Introduces a second-order method for zeroth-order stochastic convex bandits.
result Regret bound of ( 1 + r / d ) [ d 1.5 n + d 3 ] p o l y l o g ( n , d , r ) (1 + r/d)[d^{1.5} \sqrt{n} + d^3] polylog(n, d, r) ( 1 + r / d ) [ d 1.5 n + d 3 ] p o l y l o g ( n , d , r ) . RONM method reduces regret in stochastic convex bandits with decreasing noise.
problem Stochastic convex bandit problem with decreasing noise.
method Regularized Online Newton Method (RONM) based on Online Newton Method (ONM).
result RONM achieves polylogarithmic regret in time horizon n.
Improved regret bounds for Tsallis-INF in adversarial bandits and corruptions.
problem Adversarial bandits and corruptions in multiarmed bandit problems.
method Improved regret bounds for Tsallis-INF algorithm.
result Achieves $\mathcal{O}\left(\left(\sum_{i
eq i^*} \frac{1}{Δ_i}
ight)\log_+\left(\frac{(K-1)T}{\left(\sum_{i
eq i^*} \frac{1}{Δ_i}
ight)^2}
ight)+\sqrt{C\left(\sum_{i
eq i^*}\frac{1}{Δ_i}
ight)\log_+\left(\frac{(K-1)T}{C\sum_{i
eq i^*}\frac{1}{Δ_i}}
ight)}
ight)$ regret bound.
A new algorithm reduces regret in cooperative multi-agent bandits with heavy-tailed data.
problem Cooperative multi-agent bandits with heavy-tailed data.
method MP-UCB algorithm incorporating robust estimation with message-passing protocol.
result Optimal regret bounds for MP-UCB in various settings.
Combines multiple bandit algorithms to create a nearly optimal single algorithm.
problem Designing a single bandit algorithm that performs nearly as well as the best individual algorithm in a stochastic environment.
method Develops two general corralling algorithms that achieve favorable regret guarantees.
result The regret of the corralling algorithms is no worse than the best individual algorithm's performance.
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.
Paper tackles stochastic k k k -submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k k k -submodular functions with full-bandit feedback. method Proposes online algorithms for various k k k -submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α α α -regret bounds for multiple k k k -submodular stochastic combinatorial multi-armed bandit problems. Study on policy gradient for stochastic bandits using diffusion approximation.
problem Improving policy gradient methods for stochastic bandits with optimal regret bounds.
method Continuous-time diffusion approximation of policy gradient with learning rate analysis.
result Proved optimal regret bound of O ( k log ( k ) log ( n ) / η ) O(k \log(k) \log(n) / η) O ( k log ( k ) log ( n ) / η ) for η = O ( Δ 2 / log ( n ) ) η= O(Δ^2/\log(n)) η = O ( Δ 2 / log ( n )) . A new algorithm improves stochastic linear bandit performance using residual bootstrap.
problem Improving performance in stochastic linear bandit problems.
method Residual bootstrap exploration to estimate mean reward and pull the arm with the highest estimate.
result Proposed algorithm exttt{LinReBoot} achieves high-probability sub-linear regret under mild conditions.
Stochastic multi-armed bandits form a class of online learning problems that have important applications in online recommendation systems, adaptive medical treatment, and many others. Even though potential attacks against these learning algorithms may hijack their behavior, causing catastrophic loss in real-world appli…
Study on Pareto optimality in multi-objective bandit problems.
problem Pareto optimality in multi-objective multi-armed bandit problems.
method Formulated adversarial multi-objective multi-armed bandit, defined Pareto regrets, presented algorithms, established upper and lower bounds.
result New algorithms are optimal in adversarial settings and nearly optimal in stochastic settings.
Paper proposes efficient algorithms for bandit problems with costly sampling.
problem Maximizing expectation function over a finite set with high sampling cost.
method Proposes naive and adaptive stochastic bandit algorithms for PAC solution.
result Adaptive algorithm outperforms naive in terms of number of samples.
First robust bandit algorithm for contextual bandits with sub-linear regret.
problem Vulnerability of linear contextual bandit algorithms to adversarial attacks.
method Proposes a robust bandit algorithm for stochastic linear contextual bandits under fully adaptive and omniscient attacks.
result Sub-linear regret under various attacks without requiring attack information.
Study shows efficient neural network approach for stochastic bandits.
problem Optimizing decisions in uncertain environments with neural network models.
method OFU-ReLU algorithm that balances exploration and exploitation, using a transformed feature space.
result Achieves i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret guarantee for stochastic bandits with ReLU neural networks. We study "adversarial scaling", a multi-armed bandit model where rewards have a stochastic and an adversarial component. Our model captures display advertising where the "click-through-rate" can be decomposed to a (fixed across time) arm-quality component and a non-stochastic user-relevance component (fixed across arms…
New algorithm tackles delayed feedback in Lipschitz bandits with sublinear regret.
problem Delayed feedback in Lipschitz bandits.
method Design of algorithms for bounded and unbounded stochastic delays.
result Sublinear regret guarantees for both bounded and unbounded delays.
Meta-learning improves performance in stochastic linear bandits.
problem Selecting a learning algorithm that performs well across multiple bandit tasks.
method Regularized OFUL algorithm with a bias vector, estimating bias within the learning-to-learn setting.
result Meta-learning strategies improve performance when the number of tasks grows and task variance is small.
New algorithms tackle RKHS bandits with reduced complexity and improved performance.
problem Adversarial and stochastic RKHS bandit problems with high computational complexity.
method Combining approximation theory with misspecified linear bandit methods.
result First general algorithm for adversarial RKHS bandit problem.
New algorithms protect user data while optimizing personalized decisions.
problem Personalized decision-making with private user data.
method Developed LDP algorithms for stochastic generalized linear bandits using SGD and OLS.
result Achieved the same regret bound as non-privacy settings with LDP.
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.
Paper addresses privacy and robustness in stochastic linear bandits.
problem Stochastic linear bandits with differential privacy and adversarial robustness.
method Logarithmic batch queries, arm elimination algorithm, two privacy models.
result First algorithms providing differential privacy and adversarial robustness.
Balances and eliminates base algorithms in bandits and RL to bound total regret.
problem Model selection in bandits and reinforcement learning with unknown optimal regret.
method Balances and eliminates base algorithms based on candidate regret bounds.
result Total regret bound is the best valid candidate regret bound times a small multiplicative factor.
New algorithm tackles stochastic bandits with varying arm-dependent delays.
problem Applying existing algorithms to stochastic delayed bandit settings is restricted by strong assumptions on delay distributions.
method Proposes a simple UCB-based algorithm called PatientBandits that weakens assumptions on delay distributions.
result Provides bounds on regret and performance lower bounds for the PatientBandits algorithm.
We study adversarial attacks that manipulate the reward signals to control the actions chosen by a stochastic multi-armed bandit algorithm. We propose the first attack against two popular bandit algorithms: ε ε ε -greedy and UCB, \emph{without} knowledge of the mean rewards. The attacker is able to spend only logarithmic …
Unified framework for high-dimensional bandit problems with low-dimensional structures.
problem Stochastic high-dimensional bandit problems with low-dimensional structures.
method Proposed a simple unified algorithm and a general analysis framework for the regret upper bound.
result Unified algorithm achieves comparable regret bounds in various high-dimensional bandit problems.
Data that is gathered adaptively --- via bandit algorithms, for example --- exhibits bias. This is true both when gathering simple numeric valued data --- the empirical means kept track of by stochastic bandit algorithms are biased downwards --- and when gathering more complicated data --- running hypothesis tests on c…
A new batch ensemble method reduces regret in stochastic bandits.
problem Efficiently balancing exploration and exploitation in online RL.
method Proposes a batch ensemble scheme to achieve near-optimal regret.
result Proves near-optimal regret with a single parameter independent of variance.
New algorithms improve linear bandit performance with low computation.
problem Optimizing reward in linear stochastic bandits.
method Reward-biased maximum likelihood method modified for linear and generalized linear bandits.
result New policies achieve order-optimality and competitive empirical performance.
New algorithm reduces regret with diverse contexts in bandits.
problem Impact of context diversity on stochastic linear contextual bandits.
method Design of LinUCB-d algorithm and analysis of its regret performance.
result Cumulative expected regret is bounded by a constant under diverse context assumption.
New algorithm for efficiently identifying the best arm in stochastic bandits.
problem Best arm identification in stochastic multi-armed bandits with fixed confidence.
method Sequential probability ratio tests for arm selection.
result Asymptotically optimal sample complexity and guaranteed δ − δ- δ − PAC performance. New method reduces ensemble size for linear bandits, achieving near optimal regret.
problem Achieving near optimal regret in linear bandits with limited ensemble size.
method Ensemble sampling with a size of order d log T d \log T d log T for a d d d -dimensional stochastic linear bandit. result Regret is at most ( d log T ) 5 / 2 T (d \log T)^{5/2} \sqrt{T} ( d log T ) 5/2 T , improving over linear scaling with T T T . Paper tackles good arm identification in stochastic bandits.
problem Identifying good arms with minimal samples.
method Proposes DGAI, a differentiable algorithm to improve sample complexity.
result DGAI outperforms baseline algorithms in synthetic and real-world datasets.
The study analyzes batched methods for early stopping in stochastic multi-armed bandits.
problem Early stopping in stochastic multi-armed bandits with fixed confidence.
method Instance-dependent lower bounds and a general batched algorithm with upper bounds.
result Upper and lower bounds on the number of batches and sample complexity.
New algorithm optimizes dueling bandits for both stochastic and adversarial preferences.
problem Optimizing decision-making in environments where only relative preferences are observed.
method Proposed a reduction from dueling bandits to multi-armed bandits, achieving optimal regret bounds.
result First best-of-both-world result for dueling bandits, optimal regret bound for Condorcet-winner benchmark.
New algorithm improves learning efficiency in multi-task contextual bandits.
problem Improving learning efficiency in multi-task contextual bandits.
method Alternating projected gradient descent (GD) and minimization estimator for low-rank feature matrix recovery.
result Proved regret bound for multi-task learning algorithm.
New bandit model for e-commerce with ordered categories.
problem Optimizing customer experience in e-commerce with unknown preferences.
method Introducing three types of ordering between categories and proving lower bounds on cumulative regret.
result Proved that algorithms can fully leverage the structure of the model with theoretical guarantees.
A new algorithm tackles graph-based contextual bandits with efficient regret bounds.
problem Predicting labels on graphs with contextual bandit methods.
method Graph-based contextual bandit algorithm using optimal stochastic bandit techniques.
result Regret bounds for line graphs and trees, and improved bounds for general graphs.
Thompson Sampling tackles noisy context in stochastic bandits.
problem Designing an action policy for noisy, corrupted contexts in stochastic bandits.
method Introducing a Thompson Sampling algorithm for Gaussian bandits with Gaussian context noise, adopting an information-theoretic analysis.
result Demonstrates the Bayesian regret of the proposed algorithm concerning the oracle's action policy.
Motivated by applications of bandit algorithms in education, we consider a stochastic multi-armed bandit problem with ε \varepsilon ε -contaminated rewards. We allow an adversary to give arbitrary unbounded contaminated rewards with full knowledge of the past and future. We impose the constraint that for each time t t t the…
This paper addresses missing covariates in stochastic linear bandits, providing a high-probability regret bound.
problem Effect of missing covariates on regret in stochastic linear bandit algorithms.
method Proposes an algorithm that provides a high-probability upper bound on regret in terms of covariate sampling probabilities.
result Regret degrades due to missingness by at most ζ m i n 2 ζ_{min}^2 ζ min 2 , where ζ m i n ζ_{min} ζ min is the minimum probability of observing covariates. We analyze how batch learning impacts bandit problems.
problem Impact of batch learning in stochastic bandits.
method Policy-agnostic regret analysis, upper and lower bounds demonstration.
result The impact of batch learning can be measured in terms of online behavior.
Paper proposes DG-ETC for online submodular maximization with stochastic bandit feedback.
problem Online unconstrained submodular maximization with stochastic bandit feedback.
method Double-Greedy - Explore-then-Commit (DG-ETC) approach.
result DG-ETC achieves logarithmic regret O ( d log ( d T ) ) O(d\log(dT)) O ( d log ( d T )) for 1 / 2 1/2 1/2 -approximate pseudo-regret. New algorithm for combinatorial bandit problems reduces regret.
problem Optimal selection of sets of arms in bandit problems.
method SGB algorithm with optimized exploration of unselected arms.
result Achieves ( 1 − 1 / e ) (1-1/e) ( 1 − 1/ e ) -regret bound of O ( n 1 3 k 2 3 T 2 3 log ( T ) 2 3 ) \mathcal{O}(n^{\frac{1}{3}} k^{\frac{2}{3}} T^{\frac{2}{3}} \log(T)^{\frac{2}{3}}) O ( n 3 1 k 3 2 T 3 2 log ( T ) 3 2 ) .