Paper proposes no-regret algorithms for private GP bandit optimization.
problem Private Gaussian process bandit optimization.
method Combines uniform kernel approximator with random perturbations for differentially private GP bandit algorithms.
result Provable no-regret algorithms for stationary kernel functions in two DP settings.
Explearn learns to explain predictions using Gaussian Processes.
problem Learning to explain predictions effectively.
method Gaussian Processes-based contextual bandits.
result Guaranteed convergence with high probability.
A new algorithm uses concavity in Gaussian processes to optimize decisions in bandit problems.
problem Optimizing decisions in sequential problems with context-dependent rewards.
method Proposes a UCB algorithm using a shape-constrained reward function estimator based on a Gaussian Process model with concavity constraints.
result Derives regret bounds for the proposed UCB algorithm.
New acquisition function for extreme rewards in bandits.
problem Online decision making with extreme payoffs in multi-armed bandits.
method Modeling payoffs as Gaussian processes and using a novel UCB acquisition function.
result Demonstrated benefits across synthetic and real-world benchmarks.
Safe Gaussian Process Bandit Optimization with sub-linear regret bounds.
problem Sequential decision-making under uncertainty and safety constraints.
method Developed SGP-UCB, a safe variant of GP-UCB with modifications to respect safety constraints.
result First sub-linear regret bounds for safe Gaussian Process Bandit Optimization.
Study lenient regret and good-action identification in Gaussian process bandits.
problem Optimizing function values above a certain threshold in Gaussian process bandits.
method Study lenient regret notions and introduce algorithms for finding good actions.
result Upper and lower bounds on lenient regret for GP-UCB and elimination algorithms.
This paper studies adversarial attacks on Gaussian process bandits.
problem Adversarial attacks on Gaussian process bandits to manipulate optimal function regions.
method Proposes various adversarial attack methods on GP bandits, including white-box and black-box attacks.
result Adversarial attacks can force GP bandits to optima in target regions even with low attack budgets.
Optimal simple regret bound for Gaussian Process bandits.
problem Sequential optimization of expensive-to-evaluate functions.
method Proved a bound on simple regret for pure exploration algorithms.
result Order optimal bound on simple regret for Gaussian Process bandits.
Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.
problem Minimizing regret in Gaussian process bandits with unknown reward functions.
method New upper bound on maximum posterior variance, refined MVR and PE algorithms.
result Optimal regret bounds for noiseless, varying noise, and RKHS norms.
Robust algorithm optimizes corrupted Gaussian process bandits.
problem Sequential optimization of corrupted, expensive reward functions.
method Robust GP Phased Elimination (RGP-PE) algorithm.
result Algorithm balances robustness to corruptions with exploration and exploitation.
A batched Gaussian Process bandit optimization method achieves near-optimal regret bounds.
problem Black-box optimization with limited function evaluations.
method Batched Gaussian Process bandit optimization algorithm.
result Achieves near-optimal cumulative regret bound of O ∗ ( T γ T ) O^\ast(\sqrt{Tγ_T}) O ∗ ( T γ T ) using O ( log log T ) O(\log\log T) O ( log log T ) batches. Two algorithms improve GP bandits by selecting priors and minimizing regret.
problem Selecting appropriate GP priors for unknown functions.
method Developed two algorithms: Prior-Elimination GP-TS and HyperPrior GP-TS.
result Established sublinear regret bound for HyperPrior GP-TS.
New algorithm for recommending best arms with aggregated feedback.
problem Finding the best arm under aggregated feedback when precise rewards are unavailable.
method Gaussian Process Optimistic Optimisation (GPOO) algorithm with adaptive tree construction.
result The proposed algorithm achieves new simple regret bounds with aggregated feedback.
The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his operability over a continuous domain. The theoretical framework applies to functions u…
Paper establishes lower bounds for Gaussian process bandit optimization under various perturbation models.
problem Lower bounds for Gaussian process bandit optimization in noisy and robust settings.
method Novel proof techniques for standard and robust settings, including deterministic strategies.
result Demonstrates inevitable joint dependence of cumulative regret on corruption level and time horizon in robust settings.
A new method optimizes in nonstationary environments with many arms efficiently.
problem Optimizing in nonstationary environments with a large number of arms.
method Gaussian interpolation to learn continuous Lipschitz reward functions in nonstationary environments.
result Efficiently learns continuous Lipschitz reward functions with O ∗ ( T ) \mathcal{O}^*(\sqrt{T}) O ∗ ( T ) cumulative regret. The paper improves bounds on regret in Gaussian process bandits.
problem Sequential optimization of expensive, possibly non-convex functions with noisy feedback.
method Analyzes maximal information gain and decay rates of GP kernel eigenvalues to improve regret bounds.
result General bounds on maximal information gain and improved regret bounds for various settings, including Matérn kernels.
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.
Proposes sampling from reverse diffusion posteriors for contextual bandits.
problem Complex distributions in contextual bandits.
method Approximate posterior sampling with a diffusion model prior using Laplace approximation.
result Empirically consistent and efficient approximations for contextual bandits.
Algorithm optimizes collaborative learning among distributed clients using kernel-based bandits.
problem Optimizing personalized objectives in a distributed system with limited global information.
method Kernel-based bandit framework with surrogate Gaussian process models, sparse approximations.
result Order-optimal regret performance (up to polylogarithmic factors) and reduced communication overhead.
New algorithms for optimizing functions with noisy feedback, even when the model is misspecified.
problem Optimizing a black-box function with noisy bandit feedback, especially when the model is misspecified.
method Developed two algorithms based on Gaussian process methods: EC-GP-UCB and Phased GP Uncertainty Sampling.
result Achieved optimal dependence on misspecification error without prior knowledge, and effective in stochastic contextual settings.
The paper offers efficient algorithms for combinatorial and linear bandits using empirical process theory.
problem Optimal algorithms for combinatorial and linear bandits with practical sample complexity.
method Empirical process theory, Gaussian-width, minimizing experimental design objective.
result Sample complexity matches lower bounds, especially for combinatorial classes.
New method reduces GP bandit complexity while maintaining good performance.
problem Computational burden in Bayesian optimization with Gaussian processes.
method Information thresholding to compress GP posterior and reduce complexity.
result Sublinear regret bounds with sublinear posterior complexity.
New experimental design minimizes regret in bandits.
problem Minimizing regret in online stochastic linear and combinatorial bandits.
method Experimental design-based algorithm balancing information gain and reward.
result State-of-the-art finite time regret guarantees and computational efficiency.
New algorithm optimizes noisy, potentially corrupted functions.
problem Optimizing unknown functions with noisy bandit feedback, especially when evaluations are corrupted.
method Fast-Slow GP-UCB algorithm, combining robust and non-robust evaluations, enlarged confidence bounds.
result Theoretical analysis upper bounds cumulative regret, showing dependencies on corruption level and kernel.
A new algorithm balances global reward and group constraints in federated multi-armed bandits.
problem Maximizing global reward while protecting client privacy in federated learning.
method Combinatorial contextual bandit with group constraints, using a two-output Gaussian process.
result TCGP-UCB incurs low regret, balancing super arm reward and group reward constraints.
Algorithm optimizes bandit decisions with changing action sets using Gaussian processes.
problem Optimizing decisions in a bandit problem with time-varying action sets.
method Proposes an algorithm called O'CLOK-UCB using Gaussian processes to handle changing action sets and contexts.
result Achieves regret bound of i l d e O ( λ ∗ ( K ) K T γ K T ( ∪ t ≤ T X t ) ) ilde{O}(\sqrt{λ^*(K)KTγ_{KT}(\cup_{t\leq T}\mathcal{X}_t)} ) i l d e O ( λ ∗ ( K ) K T γ K T ( ∪ t ≤ T X t ) ) with high probability. Gaussian prior and likelihood improve bandit learning performance.
problem Improving bandit learning with misspecified Gaussian distributions.
method An agent with a bounded information ratio interacts with a Bernoulli bandit based on a Gaussian prior and likelihood.
result The regret increase is at most linear in the square-root of the time horizon for diffuse distributions.
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.
Method predicts future rewards from past actions in a linear Gaussian system.
problem Maximizing cumulative reward in a stochastic multi-armed bandit with linear Gaussian dynamics.
method Proposes a method using a modified Kalman filter to predict future rewards based on past rewards.
result Reward from any action can be used to predict another action's future reward.
Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.
problem Limited understanding of self-normalized concentration for vector-valued processes outside sub-Gaussian frameworks.
method Developed concentration inequalities for self-normalized processes with light tails (e.g., Bennett, Bernstein bounds) for vector-valued data.
result Provided new insights and bounds for self-normalized processes with non-sub-Gaussian distributions.
This paper analyses the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al., 2010). For GPs with Gaussian observation noise, with variance strictly greater than zero, (Srinivas et al., 2010) pro…
This paper analyzes the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al, 2010). For GPs with Gaussian observation noise, with variance strictly greater than zero, Srinivas et al proved that t…
No-regret optimization for time-varying functions using uncertainty injection.
problem Optimizing time-varying functions with no-regret in bandit feedback.
method W-SparQ-GP-UCB, incorporating uncertainty injection and additional queries.
result Achieves no-regret with a vanishing number of additional queries per iteration.
Solves action selection for large spaces in RL, achieving near-optimal performance.
problem Selecting a small, representative subset of actions from a large, shared action space.
method Extends meta-bandit approach to MDPs, using a relaxed sub-Gaussian process model.
result Achieves performance comparable to full action space, with theoretical guarantees.
We consider the sequential Bayesian optimization problem with bandit feedback, adopting a formulation that allows for the reward function to vary with time. We model the reward function using a Gaussian process whose evolution obeys a simple Markov model. We introduce two natural extensions of the classical Gaussian pr…
Thompson Sampling bounds for contextual bandits with sub-Gaussian rewards.
problem Improving the performance of Thompson Sampling in contextual bandits with sub-Gaussian rewards.
method Proved comprehensive bounds on Thompson Sampling expected cumulative regret based on mutual information and lifted information ratio for sub-Gaussian rewards.
result Explicit regret bounds for various contextual bandit scenarios.
BIS uses bandits to efficiently sample from expensive-to-evaluate densities.
problem Sampling from computationally expensive target densities.
method Sequential selection through multi-armed bandits, optimizing sample set directly.
result BIS achieves accurate sampling with fewer evaluations than adaptive methods.
Stochastic Lipschitz bandit algorithms balance exploration and exploitation, and have been used for a variety of important task domains. In this paper, we present a framework for Lipschitz bandit methods that adaptively learns partitions of context- and arm-space. Due to this flexibility, the algorithm is able to effic…
We study the recovering bandits problem, a variant of the stochastic multi-armed bandit problem where the expected reward of each arm varies according to some unknown function of the time since the arm was last played. While being a natural extension of the classical bandit problem that arises in many real-world settin…
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. New BO method optimizes functions efficiently even with unknown hyperparameters.
problem Inaccurate estimation of Gaussian process hyperparameters degrades BO performance.
method Exploits multi-armed bandit and novel training loss function for consistent hyperparameter estimation.
result Sub-linear convergence to global optimum with unknown hyperparameters.
Optimizes arm selection with side information in Gaussian bandits.
problem Optimizing arm selection with side information in Gaussian bandits.
method Constructs an LP-based asymptotic instance-dependent lower bound on the regret and develops the first known asymptotically optimal algorithm.
result First known asymptotically optimal algorithm for Gaussian bandits with side information.
NK bandits improve performance on nonlinear tasks.
problem Improving performance on nonlinear sequential decision tasks.
method Proposed NK bandits using neural kernels to guide policies.
result NK bandits achieve state-of-the-art performance.
In this paper, the problem of maximizing a black-box function f : X → R f:\mathcal{X} \to \mathbb{R} f : X → R is studied in the Bayesian framework with a Gaussian Process (GP) prior. In particular, a new algorithm for this problem is proposed, and high probability bounds on its simple and cumulative regret are established. The query po…
ES reduces high-probability regret in stochastic linear bandits.
problem High-probability regret in stochastic linear bandits.
method Linear ensemble sampling with standard Gaussian perturbations, analyzing m = Θ ( d log n ) m=Θ(d\log n) m = Θ ( d log n ) ensemble size. result ES achieves i l d e O ( d 3 / 2 n ) ilde O(d^{3/2}\sqrt n) i l d e O ( d 3/2 n ) high-probability regret, closing the gap to Thompson sampling. ERTS uses Thompson sampling for Gaussian entropic risk bandits, achieving regret bounds.
problem Risk in decision making complicates reward maximization in MAB problems.
method ERTS (Entropic Risk Thompson Sampling) using Thompson sampling with an entropic risk measure.
result Regret bounds for ERTS under entropic risk measure provided.
Polynomial-time method solves complex combinatorial semi-bandits.
problem Optimal strategies for combinatorial semi-bandits with uncorrelated Gaussian rewards.
method Proposes a polynomial-time method to solve the Graves-Lai optimization problem for various combinatorial structures.
result First known approach to implement asymptotically optimal algorithms in polynomial time for combinatorial semi-bandits.