New approach reduces unconstrained linear bandits to simpler optimization problems.
problem Unconstrained linear bandits problem.
method Perturbation-based approach combined with comparator-adaptive OLO algorithms.
result First high-probability guarantees for both static and dynamic regret in unconstrained linear bandits.
New algorithm minimizes cumulative loss in dynamic linear bandits without prior knowledge of comparator switches.
problem Minimizing cumulative loss in dynamic linear bandits with unknown number of switches.
method Combining several bandit algorithms to adapt to unknown number of switches without prior knowledge.
result First algorithm achieving optimal regret guarantee of O ( d ( 1 + S T ) T ) \mathcal{O}\big(\sqrt{d(1+S_T) T}\big) O ( d ( 1 + S T ) T ) up to poly-logarithmic terms. 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. LinConTS improves regret and constraint violations in probabilistic linearly constrained bandits.
problem Maximizing cumulative reward under probabilistic linear constraints.
method LinConTS, a Thompson Sampling-based algorithm for bandits with linear constraints.
result LinConTS achieves O(log T) regret and constraint violations for suboptimal arms.
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. 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 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 ) . New algorithm tackles batched stochastic linear bandits with 1-bit communication constraints.
problem Stochastic linear bandits with 1-bit communication constraints.
method Phased-elimination algorithms based on G-optimal designs and 1-bit mean estimation.
result Achieves near-optimal regret bounds for broad scaling regimes.
Agents cooperate to make decisions in multi-armed bandits over a graph.
problem Optimizing decisions in multi-agent multi-armed bandits with shared information.
method Designs consensus-based distributed estimation and cooperative algorithms for group decision-making.
result Achieves group performance close to centralized fusion center.
New lower bound shows bandit convex optimization is harder than previously thought.
problem Establishing a lower bound on the minimax expected regret for bandit convex optimization.
method Constructing a hard class of convex functions and analyzing the posterior spread of Fisher information matrices.
result A Ω ~ ( d 5 / 4 T ) \widetildeΩ(d^{5/4}\sqrt{T}) Ω ( d 5/4 T ) lower bound on the minimax expected regret. A new optimization algorithm improves convergence in unconstrained problems.
problem Unconstrained optimization problems.
method Element-wise relaxed scalar auxiliary variable (E-RSAV) algorithm.
result Improved convergence and alignment of modified and original energy.
Paper tackles best mixed arm identification with cost constraints in bandit models.
problem Finding the best mixed arm with cost constraints in a stochastic bandit model.
method Proposes SFSR algorithm combining successive reject and score-function-based rejection criteria.
result Upper and lower bounds on mis-identification probability show exponential decay with budget.
Our paper explains deep neural collapse in multiple layers.
problem Understanding deep neural collapse in multi-layered neural networks.
method Generalized unconstrained features model for deep networks.
result Deep unconstrained features model exhibits deep neural collapse.
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.
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 ) . Paper tackles constrained bandit problems with a new learning framework.
problem Optimizing a black-box reward function subject to a black-box constraint function over a continuous space.
method Rectified Pessimistic-Optimistic Learning (RPOL) framework, incorporating optimistic and pessimistic GP bandit learning.
result RPOL achieves sublinear regret and minimal cumulative constraint violation.
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.
Develops parameter-free online mirror descent for optimal dynamic regret.
problem Optimal online linear optimization in unbounded domains.
method Modified online mirror descent framework for parameter-free algorithms.
result First unconstrained online linear optimization achieving optimal dynamic regret.
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.
Paper tackles LDP bandits learning with improved results and sub-linear regret.
problem Contextual bandits learning with LDP privacy constraints.
method Simple black-box reduction frameworks for context-free bandits, extended to GLB.
result First result for BCO with multi-point feedback under LDP, sub-linear regret for GLB.
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.
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 method parameterizes solutions to linearized vacuum constraints on Einstein manifolds.
problem Parameterizing solutions to linearized vacuum constraints on Einstein manifolds.
method Parameterize solutions using unconstrained potentials and shield linearized gravitational fields.
result Showed how to shield linearized gravitational fields without TT gauge for any value of cosmological constant.
Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.
problem Adversarial combinatorial bandits with general non-linear reward functions.
method Extending existing work on adversarial linear combinatorial bandits, analyzing minimax optimal regret for polynomial and non-polynomial reward functions.
result Minimax optimal regret bounds for adversarial combinatorial bandits with general non-linear reward functions.
Unified approach for non-stationary linear bandits with dynamic regret.
problem Non-stationary linear bandits with round-specific feasible actions and drifting reward models.
method Unified misspecification-reduction viewpoint, restarting algorithms with misspecification-dependent regret guarantees.
result Optimal \(T^{2/3}P_T^{1/3}\) dynamic-regret dependence for both linear bandits and contextual linear bandits.
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.
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.
Optimizes pure exploration in linear bandits with a new algorithm.
problem Best-arm identification in linear stochastic bandits.
method Developed the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits.
result Avoids the pitfall of a simple but difficult instance and bypasses the need to solve an optimal design problem.
This paper achieves optimal regret bounds for locally private linear contextual bandit.
problem Designing locally private linear contextual bandit algorithms with optimal regret bounds.
method New algorithmic and analytical ideas, including mean absolute deviation analysis and layered principal component regression.
result Achieves an i l d e O ( T ) ilde O(\sqrt{T}) i l d e O ( T ) regret upper bound for locally private linear contextual bandit. 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. New algorithm for partially observable contexts in finance.
problem Decision making based on partially observable, correlated market information.
method EMKF-Bandit algorithm integrating system identification, filtering, and bandit algorithms.
result Sub-linear regret under conditions on filtering.
Algorithm balances online and offline data for linear bandits.
problem Online learning with an offline dataset in linear bandits.
method Proposes a linear bandit algorithm that uses offline data early and increasingly favors exploration as the horizon grows.
result Establishes regret bounds showing competitive performance with both purely online and offline solutions.
A new algorithm for conversational recommendation systems using dueling bandits in GLMs.
problem Limited user feedback in existing conversational bandit methods.
method Integrates dueling bandits with relative feedback in generalized linear models.
result Theoretical and empirical validation of ConDuel's efficacy.
The paper tightens the regret rate for linear bandit problems.
problem Bayesian regret in linear bandit problems.
method Information-theoretic framework and chaining argument.
result Established a new bound with a tight rate of O ( d T ) O(d\sqrt{T}) O ( d T ) . Modified Meta-TS for linear contextual bandits reduces regret.
problem Optimizing decision-making in dynamic environments with context vectors.
method Meta-TSLB algorithm for linear contextual bandits, analyzing Bayes regret.
result Derives an O ( ( m + log ( m ) ) n log ( n ) ) O((m+\log(m))\sqrt{n\log(n)}) O (( m + log ( m )) n log ( n ) ) bound on Bayes regret. GLCB uses Gated Linear Networks for online contextual bandits.
problem Online learning in contextual bandits with uncertainty estimation.
method Gated Linear Networks (GLNs) for prediction and uncertainty estimation.
result GLCB outperforms state-of-the-art methods in online contextual bandits.
New algorithms minimize regret in multi-task and lifelong linear bandits with shared representation.
problem Minimizing regret in multi-task and lifelong linear bandits with shared representation.
method Novel algorithms using efficient estimator for low-rank linear feature extractor and novel analysis.
result Achieved regret bounds matching minimax lower bound up to logarithmic factors.
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.
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the predictions of the optimal comparator are invariant under any linear transformation of th…
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.
This article introduces the concepts around Online Bandit Linear Optimization and explores an efficient setup called SCRiBLe (Self-Concordant Regularization in Bandit Learning) created by Abernethy et. al.\cite{abernethy}. The SCRiBLe setup and algorithm yield a O ( T ) O(\sqrt{T}) O ( T ) regret bound and polynomial run time comple…
We study the neural-linear bandit model for solving sequential decision-making problems with high dimensional side information. Neural-linear bandits leverage the representation power of deep neural networks and combine it with efficient exploration mechanisms, designed for linear contextual bandits, on top of the last…
BLAE solves batched linear bandits with optimal regret and practical performance.
problem Batched linear bandit problem with limited adaptivity.
method Integrates arm elimination with regularized G-optimal design, achieving minimax optimal regret.
result Achieves minimax optimal regret in both large- K K K and small- K K K regimes with O ( log log T ) O(\log\log T) O ( log log T ) batches. Study linear contextual bandits with confounded offline data, improving regret bounds.
problem Linear contextual bandits with confounded offline data.
method Construct a linear bandit algorithm that utilizes projected information.
result Proved regret bounds that improve current bounds by a factor related to visible dimensionality.
An algorithm for maximizing rewards under linear cost constraints.
problem Maximizing rewards while adhering to cost constraints in a linear bandit problem.
method Proposes an upper-confidence bound algorithm called optimistic pessimistic linear bandit (OPLB) for constrained contextual linear bandits.
result Proves an O ~ ( d T τ − c 0 ) \widetilde{\mathcal{O}}(\frac{d\sqrt{T}}{τ-c_0}) O ( τ − c 0 d T ) bound on regret for the proposed algorithm. This paper tackles efficient federated learning for generalized linear bandits.
problem Limited communication efficiency restricts existing federated learning solutions to linear models.
method Proposes a communication-efficient solution framework using online and offline regression.
result Proves sub-linear regret and communication cost for generalized linear bandits.
Bayesian optimization improved for biased data.
problem Adversarial bias in observations, especially hidden confounders.
method Reduction to dueling bandits, information-directed sampling (IDS).
result First efficient kernelized algorithm with regret guarantees.
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.