New framework for Adam-type algorithms with constant β1, improving regret analysis.
problem Theoretical vs. practical use of Adam and variants with constant β1.
method Proposed a novel framework to derive optimal, data-dependent regret bounds with constant β1.
result Optimal, data-dependent regret bounds with constant β1 are achievable without further assumptions.
Improved analysis of UCRL2 with empirical Bernstein inequality reduces exploration-exploitation regret.
problem Exploration-exploitation in communicating Markov Decision Processes.
method Analysis of UCRL2 with Empirical Bernstein inequalities (UCRL2B).
result Regret bound of O ~ ( D Γ S A T ) \widetilde{O}(\sqrt{DΓS A T}) O ( D Γ S A T ) for UCRL2B. Improved dynamic regret analysis for strongly convex and smooth functions.
problem Analyzing dynamic regret for online learning algorithms.
method Improved analysis of the Online Multiple Gradient Descent (OMGD) algorithm.
result Achieved a best-of-three-worlds guarantee for dynamic regret.
Optimistic Hedge achieves optimal regret bounds in two-player zero-sum games.
problem Achieving optimal regret bounds for optimistic Hedge in two-player zero-sum games.
method Refined regret analysis and optimization problem formulation.
result Optimistic Hedge achieves O ( log m log n ) O(\sqrt{\log m \log n}) O ( log m log n ) regret bounds, matching upper and lower bounds. SCaLE tackles dynamic regret in noisy bandit feedback with switching costs.
problem Unbounded metric movement costs in bandit online convex optimization.
method SCaLE algorithm for high-dimensional dynamic quadratic hitting costs and ℓ 2 \ell_2 ℓ 2 -norm switching costs, with spectral regret analysis. result First algorithm achieving sub-linear dynamic regret without hitting cost knowledge.
Significant improvements in regret analysis for adaptive online learning problems.
problem Exploiting low variance in online learning problems without known variances.
method Novel peeling-based regret analysis leveraging elliptical potential `count` lemma.
result Significant improvements in regret bounds for linear bandits and linear mixture MDPs.
This paper analyzes data-driven Newsvendor problems and finds a wide range of possible regrets.
problem Guessing the number drawn from an unknown distribution with asymmetric costs.
method Unified analysis using the notion of clustered distributions and new lower bounds.
result The entire spectrum of achievable regrets from 1 / n 1/\sqrt{n} 1/ n to 1 / n 1/n 1/ n is possible. New analysis shows how temporal variability affects online learning performance.
problem Understanding the impact of temporal variability on online learning performance.
method Careful regret analysis and adaptive algorithm development.
result Proved a novel static regret bound that depends on temporal variability.
Study on regret minimization in deterministic MDPs.
problem Minimizing regret in deterministic reinforcement learning.
method Logarithmic regret lower bounds, leveraging graph theory and cycles.
result Explicitly quantifies the fundamental limit of performance achievable by any learning algorithm.
Study shows certainty equivalent policy minimizes regret in continuous-time systems.
problem Minimizing regret in continuous-time stochastic linear-quadratic systems.
method Theoretical analysis of randomized certainty equivalent policy.
result Establishes square-root of time regret bounds and linear scaling with parameters.
We prove a new minimax theorem connecting the worst-case Bayesian regret and minimax regret under partial monitoring with no assumptions on the space of signals or decisions of the adversary. We then generalise the information-theoretic tools of Russo and Van Roy (2016) for proving Bayesian regret bounds and combine th…
Unified analysis of Gaussian Process Thompson Sampling without discretization.
problem Sequential decision-making over continuous action spaces.
method Frequentist regret analysis based on fractional Gaussian process posteriors.
result Unified discretization-free regret bound for various kernel classes.
The paper tackles robust policy learning from multiple data sources.
problem Learning a policy that generalizes across diverse settings from multiple heterogeneous data sources.
method Proposes a minimax regret optimization objective and a policy learning algorithm combining doubly robust offline policy evaluation and no-regret learning.
result Achieves minimal worst-case mixture regret up to a moderated vanishing rate of the total data across all sources.
Paper achieves logarithmic regret for online Kalman filter learning.
problem Predicting observations from an unknown, partially observed linear system with stochastic noise.
method Online least-squares algorithm exploiting the approximate linearity of Kalman filter predictions.
result Achieves regret of order poly(log(N)) with high probability.
We propose algorithms for online principal component analysis (PCA) and variance minimization for adaptive settings. Previous literature has focused on upper bounding the static adversarial regret, whose comparator is the optimal fixed action in hindsight. However, static regret is not an appropriate metric when the un…
This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning algorithm is if it is allowed a one-step look-ahead into the future. We show that given…
Mirror descent with an entropic regularizer is known to achieve shifting regret bounds that are logarithmic in the dimension. This is done using either a carefully designed projection or by a weight sharing technique. Via a novel unified analysis, we show that these two approaches deliver essentially equivalent bounds …
Ensemble sampling approximates Thompson sampling for complex models.
problem Computational intractability of exact posterior distributions.
method Thompson sampling approximation with information-theoretic concepts.
result Established a first rigorous regret bound for ensemble sampling.
Improved regret bounds for structured linear contextual bandits with Gaussian noise.
problem Optimizing bandit learning algorithms for structured contexts with Gaussian perturbations.
method Proposed simple greedy algorithms for structured linear contextual bandits with Gaussian noise.
result Unified regret analysis for structured parameters with geometric quantities as bounds.
Improved Thompson Sampling reduces regret in contextual bandits and reinforcement learning.
problem Thompson Sampling's exploration is insufficient in some contexts.
method Developed Feel-Good Thompson Sampling to address exploration issues.
result Feel-Good Thompson Sampling reduces regret compared to standard Thompson Sampling.
We consider an online learning process to forecast a sequence of outcomes for nonconvex models. A typical measure to evaluate online learning algorithms is regret but such standard definition of regret is intractable for nonconvex models even in offline settings. Hence, gradient based definition of regrets are common f…
New insights into balancing reward and fairness in stochastic MAB.
problem Balancing reward and fairness in stochastic multi-armed bandits.
method Formulated a penalization framework and proposed a hard-threshold UCB-like algorithm.
result Asymptotic fairness, nearly optimal regret, better reward-fairness tradeoff.
Improved FPL algorithms for adversarial MDPs with better regret bounds.
problem Adversarial rewards and unknown transitions in MDPs.
method Refined analysis of FPL algorithms, matching current best regret bounds.
result Improved regret bounds for FPL algorithms in adversarial MDPs.
New model-free algorithm achieves similar LQR regret guarantees.
problem Model-free control of linear dynamical systems under quadratic costs.
method Online policy gradient scheme with policy space cost analysis.
result Achieves regret scaling with √T, matching model-based methods.
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. 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. Improved regret bound for linear ensemble sampling.
problem Closing the gap between theory and practice in linear ensemble sampling.
method General regret analysis framework for linear bandit algorithms, revealing a relationship with LinPHE.
result Achieves a frequentist regret bound of i l d e O ( d 3 / 2 T ) ilde{O}(d^{3/2}\sqrt{T}) i l d e O ( d 3/2 T ) for linear ensemble sampling. New algorithm reduces reinforcement learning regret by adapting to interaction variability.
problem Existing reinforcement learning methods lack adaptability to interaction variability.
method Developed a variance-adaptive optimal algorithm for MNL function approximation.
result Achieved instance-wise optimal regret bounds, validating efficiency in practice.
The paper tackles personalized policy learning from diverse data sources in a federated setting.
problem Learning personalized decision policies from observational bandit feedback across multiple heterogeneous data sources.
method Introduces a novel regret analysis for distinguishing global and local regret, and presents a federated policy learning algorithm using local policies trained with doubly robust offline policy evaluation strategies.
result Establishes finite-sample upper bounds on global and local regret, characterizing them by source heterogeneity and distribution shift.
Improved analysis of UCBVI algorithm with better empirical performance.
problem Improving the UCBVI algorithm's performance and understanding its bounds.
method Refined analysis of UCBVI algorithm with improved bonus terms and regret analysis.
result Improving multiplicative constants in UCBVI bounds enhances empirical performance.
New framework analyzes regret in guided diffusion for optimizing structured inputs.
problem Understanding regret behavior in guided-diffusion black-box optimization for structured design problems.
method Developed a certificate-based expected simple-regret framework that avoids assumptions breaking down in modern diffusion BO pipelines.
result Explains how exponential and polynomial convergence can arise from mass lift in near-optimal designs.
New method minimizes regret in AMDP with high probability.
problem Pessimistic regret analysis in AMDP.
method Developed a new policy search method achieving optimistic regret.
result Achieved sublinear optimistic regret with high probability.
We discuss a multiple-play multi-armed bandit (MAB) problem in which several arms are selected at each round. Recently, Thompson sampling (TS), a randomized algorithm with a Bayesian spirit, has attracted much attention for its empirically excellent performance, and it is revealed to have an optimal regret bound in the…
New method for semiparametric bandits reduces regret to optimal levels.
problem Complex reward structures in semiparametric bandits.
method Experimental-design approach with sharp regret bound and PAC bound.
result Minimax regret of i l d e O ( d T ) ilde{O}(\sqrt{dT}) i l d e O ( d T ) and logarithmic regret under positive suboptimality gap. Improved Thompson Sampling using fractional posteriors achieves better regret bounds.
problem Optimizing regret in stochastic multi-armed bandit problems.
method Using α \alpha α -posterior distributions, derived frequentist regret bounds. result Instance-dependent and instance-independent regret bounds established.
Paper develops robust estimators and strategies for stochastic MABs with heavy-tailed rewards.
problem Stochastic multi-armed bandits with heavy-tailed rewards.
method Proposes a novel robust estimator and perturbation-based exploration strategy.
result Develops upper and lower regret bounds for various perturbations.
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 )) . Paper introduces a new G ⋆ G^\star G ⋆ regret measure for online convex optimization with smooth losses.
problem Online convex optimization with smooth losses.
method Introduces a new G ⋆ G^\star G ⋆ regret measure that depends on the cumulative squared gradient norm. result The G ⋆ G^\star G ⋆ regret can be arbitrarily sharper than existing measures when losses have vanishing curvature. Improved risk-sensitive RL with exponential Bellman equation and better regret bounds.
problem Exponential gap between upper and lower bounds in risk-sensitive RL.
method Identified and addressed deficiencies in existing algorithms and analysis; developed novel analysis and exploration mechanism.
result Improved regret upper bounds over existing ones.
GN algorithm solves batched bandit for nondegenerate functions near-optimally.
problem Batched bandit learning for nondegenerate functions.
method Introduces Geometric Narrowing (GN) algorithm with a O ~ ( A + d T ) \widetilde{\mathcal{O}} ( A_{+}^d \sqrt{T} ) O ( A + d T ) regret bound and O ( log log T ) \mathcal{O} (\log \log T) O ( log log T ) batches. result GN achieves near optimal regret with minimal number of batches.
Extended analysis of Q-learning's efficiency, matching optimal regret.
problem Theoretical guarantees of Q-learning's efficiency and optimal regret.
method Survey of related research, detailed proof reasoning.
result Q-learning with UCB exploration achieves sample efficiency matching optimal regret.
New approach limits regret in non-stationary bandits.
problem Understanding worst case regret in time-varying bandits.
method Belief inertia argument to resist new evidence after changes.
result Linear worst case regret for classical and restarting algorithms.
The study compares uniform-price and discriminatory auctions in terms of learning difficulty.
problem Comparing the learning difficulty of uniform-price and discriminatory multi-unit auctions.
method Characterization of learning difficulty through regret minimization in both full-information and bandit feedback settings.
result Regret scales similarly for both auction formats under full-information, but uniform-price auctions can achieve faster learning rates.
Fine-grained gap-dependent regret bounds for reinforcement learning.
problem Achieving optimal regret bounds for reinforcement learning with suboptimality gaps.
method Developed novel analytical frameworks and refined algorithms for UCB-based and non-UCB-based reinforcement learning.
result Established the first fine-grained gap-dependent regret bounds for both UCB-based and non-UCB-based algorithms.
The paper extends Thompson Sampling to infinite action spaces using information theory.
problem Addressing the limitation of finite action spaces in Thompson Sampling.
method Information-theoretic analysis, extending rate-distortion theory to infinite action spaces.
result Derives a near-optimal regret bound for bandits with infinite and continuous action spaces.
This paper establishes that optimistic algorithms attain gap-dependent and non-asymptotic logarithmic regret for episodic MDPs. In contrast to prior work, our bounds do not suffer a dependence on diameter-like quantities or ergodicity, and smoothly interpolate between the gap dependent logarithmic-regret, and the $\wid…
The paper addresses frequentist regret of Linear Thompson Sampling in stochastic linear bandits.
problem The frequentist regret of Linear Thompson Sampling (LinTS) is worse than its Bayesian counterpart.
method The paper proves the fundamental nature of the frequentist regret bound for LinTS and proposes a data-driven version of LinTS to achieve minimax optimal frequentist regret.
result The frequentist regret bound for LinTS is O ~ ( d d T ) \widetilde{\mathcal{O}}(d\sqrt{dT}) O ( d d T ) , which is the best possible under certain conditions. Paper analyzes faster convergence rates for reinforcement learning from offline data.
problem Analyzing faster convergence rates for reinforcement learning from offline data.
method Fine analysis of reinforcement learning from offline data, providing fast rates for regret convergence.
result The paper provides fast rates for the regret convergence, showing that the level of exponentiation depends on the noise in the decision-making problem.