Study robust best-arm identification in linear bandits with lower bounds and algorithms.
problem Identify a near-optimal robust arm in linear bandits with adversarial actions.
method Propose instance-dependent lower bounds and both static and adaptive bandit algorithms.
result Sample complexity matches the lower bound and algorithms effectively identify robust arms.
New algorithms for best arm identification in bandits robust to misspecified parameters.
problem Inconsistent learning performance of traditional MAB algorithms when parameters are misspecified.
method Proposes two classes of asymptotically near-optimal algorithms for statistically robust MAB under fixed-budget pure exploration.
result Establishes fundamental performance limits and proposes algorithms that are asymptotically near-optimal.
New algorithm optimally identifies best arm in both stochastic and adversarial settings.
problem Best arm identification in stochastic and adversarial reward scenarios.
method Parameter-free algorithm designed to be robust to adversarial rewards and optimal in stochastic problems.
result Algorithm's error rate matches optimal bounds in stochastic problems and is robust to adversarial rewards.
A novel algorithm for best-arm identification in non-stationary linear bandits reduces error probability.
problem Non-stationary environments in A/B testing scenarios.
method Proposes a novel algorithm P1-RAGE for robust best-arm identification. result Error probability decreases as exp(−TΔ(1)2/d), demonstrating robustness to non-stationarity. Optimal best-arm identification in linear bandits reduces sampling budget.
problem Identifying the best arm with fixed confidence in stochastic linear bandits.
method A simple algorithm that tracks an optimal proportion of arm draws, updated as rarely as desired.
result The algorithm's sampling complexity matches known lower bounds, asymptotically almost surely and in expectation.
This paper studies active learning in the context of robust statistics. Specifically, we propose a variant of the Best Arm Identification problem for \emph{contaminated bandits}, where each arm pull has probability ε of generating a sample from an arbitrary contamination distribution instead of the true und…
Open problem: fixed-budget best arm identification complexity.
problem Understanding the complexity of identifying the best arm in a fixed budget setting.
method Analyzing existing results and conjectures in the fixed-confidence setting.
result Open questions remain about the fixed-budget setting.
Contextual information helps identify the best arm more efficiently.
problem Best arm identification with contextual covariate information.
method Proposed a context-aware version of the 'Track-and-Stop' strategy.
result Expected number of arm draws matches lower bound asymptotically.
New algorithm optimizes best arm identification with minimal regret.
problem Best arm identification in multi-armed bandit problems.
method Characterized Bayesian simple regret with continuity conditions of prior, proposed a simple algorithm.
result Proposed algorithm achieves rate-optimal Bayesian simple regret.
Optimal multi-fidelity best-arm identification reduces cost with better accuracy.
problem Finding the best arm with highest mean reward at minimum cost.
method Gradient-based approach with asymptotically optimal cost complexity.
result Asymptotically optimal cost complexity compared to existing methods.
Improved theoretical guarantees for Top Two algorithms.
problem Theoretical support for best arm identification with bounded distributions.
method General analysis of Top Two methods, identifying desirable properties and replacing sampling step.
result Theoretical support for Top Two algorithms with bounded distributions.
Opt-BBAI identifies the best arm with minimal batches and pulls, optimizing both sample and batch complexity.
problem Batched best arm identification (BBAI) problem, aiming to minimize policy switches and resource usage.
method Proposed Opt-BBAI algorithm, achieving near-optimal sample and batch complexity in non-asymptotic settings.
result First algorithm to achieve near-optimal sample and batch complexity in non-asymptotic settings.
Algorithm identifies best arm with prior info in structured bandits.
problem Bayesian fixed-budget best-arm identification in structured bandits.
method Prior-dependent allocations based on structure and prior information.
result Improved theoretical bounds and robust performance across diverse models.
Motivated by drug design, we consider the best-arm identification problem in generalized linear bandits. More specifically, we assume each arm has a vector of covariates, there is an unknown vector of parameters that is common across the arms, and a generalized linear model captures the dependence of rewards on the cov…
A new algorithm for identifying the best arm in linear feedback with safety constraints.
problem Identifying the best arm in linear feedback with safety constraints.
method A gap-based algorithm that ensures safety while minimizing sample complexity.
result The algorithm achieves meaningful sample complexity while ensuring safety.
Study quantile multi-armed bandits for identifying the best arm with a specified quantile level.
problem Identifying the arm with the highest quantile in multi-armed bandits with private rewards.
method Proposed a (non-private) and differentially private successive elimination algorithms for best-arm identification.
result The proposed algorithms are essentially optimal for quantile bandit problems, with finite sample complexity even for distributions with infinite support-size.
Paper tackles best arm identification with cost consideration.
problem Best arm identification with cost consideration in product development.
method Derives a theoretical lower bound and proposes algorithms CTAS and CO.
result Simple algorithms can deliver near-optimal performance.
Improved knowledge gradient (iKG) outperforms the original KG algorithm in best arm identification problems.
problem Best arm identification (BAI) problem with limitations of the original KG algorithm.
method Follows the one-step look ahead of KG but chooses the measurement that maximizes the probability of selecting the best arm.
result Improved knowledge gradient (iKG) is asymptotically optimal and easier to extend to variant BAI problems.
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-Thresholding Bandit Problem (TBP). result Asymptotically optimal algorithm for TBP.
Motivated by the task of hyperparameter optimization, we introduce the non-stochastic best-arm identification problem. Within the multi-armed bandit literature, the cumulative regret objective enjoys algorithms and analyses for both the non-stochastic and stochastic settings while to the best of our knowledge, the best…
Study best arm identification in restless bandits with unknown TPMs.
problem Identify the best arm with fixed confidence in restless bandits with unknown TPMs.
method Proposed a policy for best arm identification and proved its expected stopping time matches the lower bound.
result The state-action visitation proportions match the optimal proportions under any asymptotically optimal policy.
EB-TCε identifies the best arm with ε confidence in stochastic bandits.
problem Identifying the best arm in stochastic bandits with a fixed level of confidence.
method EB-TCε is a novel sampling rule for ε-best arm identification in stochastic bandits.
result EB-TCε is the first anytime algorithm for fixed confidence or fixed budget identification.
Study best arm identification with safety constraints in bandit problems.
problem Real-world decision-making with safety constraints.
method Analyzed linear and monotonic reward and safety constraints, proposed algorithms.
result Guaranteed safe learning in both linear and general reward/safety constraint settings.
New research shows fixed-budget best-arm identification cannot match static oracle performance.
problem Fixed-budget best-arm identification's performance limitations.
method Analysis of various adaptive and static algorithms for best-arm identification.
result For any algorithm, there exists at least one instance where the error decay rate is at most \((1 + \frac{\log(K)}{8})^{-1}\) times that of the static oracle.
New algorithm identifies best arm with optimal budget usage.
problem Identifying the arm with the highest mean reward from multiple options.
method Proposes Almost Tracking, a closed-form algorithm for anytime best arm identification.
result Proven to be rate-optimal and outperforms existing algorithms.
New algorithm finds best feasible arm in grouped bandits.
problem Finding the best arm with all attributes above a threshold.
method Feasibility Constrained Successive Rejects (FCSR) algorithm.
result FCSR identifies the best feasible arm with optimal dependence on problem parameters.
BAICS identifies best arm with fairness constraints on subpopulations.
problem Identify the best arm while ensuring fairness across subpopulations.
method Formulated and solved BAICS problem, analyzed complexity, designed algorithm.
result Algorithm's sample complexity matches theoretical lower bound.
ACOL learns constraints from human preferences in driving simulations.
problem Learning constraints from human preferences in driving simulations.
method Adaptive Constraint Learning (ACOL) algorithm for constrained linear best-arm identification.
result ACOL's sample complexity matches worst-case lower bound and is significantly tighter in the average case.
New algorithm reduces contextual bandit identification to argmax calls.
problem Best-arm identification in stochastic contextual bandits.
method Instance-optimal PAC algorithm using argmax oracle calls.
result First instance-dependent PAC sample complexity for contextual bandits.
New algorithms for streaming bandits with limited memory.
problem Optimizing decisions in a stream of uncertain outcomes with limited memory.
method Developed algorithms for minimizing regret and identifying the best arm under bounded memory constraints.
result Upper and lower bounds on sample complexity for best-arm identification algorithms.
New algorithm improves best arm identification in Bayesian settings.
problem Finding the arm with the highest mean in unknown distributions.
method Developed a variant of successive elimination algorithm.
result Achieved optimal performance in Bayesian setting with logarithmic gap.
State of the art online learning procedures focus either on selecting the best alternative ("best arm identification") or on minimizing the cost (the "regret"). We merge these two objectives by providing the theoretical analysis of cost minimizing algorithms that are also delta-PAC (with a proven guaranteed bound on th…
The paper tackles best arm identification with minimal regret in experiments.
problem Identifying the best arm with minimal regret in experiments.
method Information-theoretic techniques and Double KL-UCB algorithm.
result Achieves asymptotic optimality in identifying the best arm with minimal regret.
Study optimizes best-arm identification with minimax and Bayes strategies.
problem Efficiently identifying the best arm in fixed-budget scenarios.
method Adaptive procedure with two stages: pilot phase and minimax game.
result Single strategy is asymptotically minimax and Bayes optimal.
Optimal best-arm identification with known number of optimal arms.
problem Identifying the best arm in a multi-armed bandit with multiple optimal arms under fixed confidence.
method Deriving a new information-theoretic lower bound and proposing a modified stopping rule.
result Achieving asymptotic instance-optimality with a new lower bound and new stopping rule.
New algorithms identify best arm with less pulls, adapting to arm covariances.
problem Best arm identification under dependent and correlated arm distributions.
method Adaptive algorithms estimating arm covariances to minimize pulls.
result Substantial improvement in best arm identification over standard setting.
New algorithm identifies best arm in semiparametric bandits with near optimal efficiency.
problem Fixed-confidence Best Arm Identification in semiparametric bandits with unknown baseline shift.
method Phase-elimination algorithm based on orthogonalized regression design.
result Nearly optimal high-probability sample-complexity upper bound established.
Box Thirding identifies the best arm efficiently under limited samples.
problem Efficiently identifying the best arm with limited sampling.
method Iterative ternary comparison of arms, discarding the weakest and exploring the best.
result Achieves comparable performance to Successive Halving with less predefined parameters.
Optimal top-2 method improves best arm identification with reduced error.
problem Identifying the arm with the highest mean in a set of arms.
method A novel top-2 algorithm that pulls the empirical best arm with probability β and the challenger arm otherwise.
result The proposed algorithm matches the information theoretic lower bound on sample complexity as δ approaches 0.
VA-LUCB identifies best arm with variance constraint, achieving optimal sample complexity.
problem Identifying the best arm with variance constraint under fixed confidence.
method Parameter-free algorithm VA-LUCB, analyzing sample complexity and proving lower bounds.
result Optimal sample complexity up to a logarithmic factor in HVA, demonstrated by experiments. New algorithms improve best-arm identification with varying rewards.
problem Identifying the best arm with varying reward variances in fixed budget.
method Proposed two algorithms: SHVar for known variances, SHAdaVar for unknown variances; uses non-uniform budget allocation.
result Bounding misidentification probabilities for both algorithms.
PROBE optimizes best-arm identification with cheap proxies, improving sample complexity.
problem Fixed-confidence best-arm identification with costly rewards and correlated cheap proxies.
method PROBE uses control-variate adjustment and phase elimination to learn residual variance online.
result PROBE achieves oracle sample complexity up to a constant factor and additive calibration cost.
New strategies for identifying the best arm in bandits with decreasing variances.
problem Best arm identification in bandits with time-varying variances.
method Two policies: initial wait followed by continuous sampling, and periodic sampling with weighted average.
result Analytical guarantees and simulations show improved performance over existing methods.
New method for identifying best arm in batched multi-armed bandit problems.
problem Identifying the best arm in multi-armed bandit problems where arms are sampled in batches.
method General linear programming framework for best arm identification in batched multi-armed bandit problems.
result Demonstrated good performance in numerical studies compared to UCB-type or Thompson sampling methods.
GNA optimally identifies the best arm with small gaps.
problem Best arm identification in fixed-budget settings.
method Generalized Neyman Allocation (GNA) for asymptotically locally minimax optimal BAI.
result GNA's worst-case bounds match the lower and upper bounds in the small-gap regime.
Bayesian algorithm improves best-arm identification within fixed budget.
problem Maximizing probability of identifying optimal arm within fixed budget.
method Proposes Bayesian elimination algorithm and derives upper bound on misidentification probability.
result Upper bound on misidentification probability reflects prior quality and matches lower bound.
Optimal best arm identification for multi-objective bandits with fixed error probability.
problem Identifying the best arm for each of multiple objectives with fixed confidence.
method Surrogate proportions to sample arms at each time step, eliminating max-min optimisation.
result Asymptotically optimal algorithm for multi-objective best arm identification.
Paper tackles unknown variances in best-arm identification.
problem Identifying the best arm with unknown variances in Gaussian distributions.
method Two approaches: empirical variance plugging or adapting transportation costs.
result The impact of unknown variances is small on sample complexity.