UCRL-WVTR tackles long-term reinforcement learning with general approximations, achieving horizon-free and instance-dependent regret bounds.
problem Long-term reinforcement learning with general function approximations.
method UCRL-WVTR proposes a novel algorithm, UCRL-WVTR, with weighted value-targeted regression and a high-order moment estimator.
result Achieves horizon-free and instance-dependent regret bounds matching minimax lower bounds up to logarithmic factors.
New algorithm achieves asymptotically optimal regret without horizon dependence.
problem Horizon-free regret minimization for reinforcement learning.
method Proposes a new algorithm and proves a regret upper bound.
result Regret upper bound of \(\tilde O(\sqrt{SAK} + S^8A^3)\) with failure probability \(\delta\).
New algorithms reduce dynamic regret in online MDPs with changing losses.
problem Online MDPs with adversarial loss changes and known transitions.
method Dynamic regret measure, novel ensemble algorithms for three models.
result Provably optimal dynamic regret bounds for episodic SSP, improved bounds for predictable environments.
This paper improves Thompson Sampling for complex decision-making problems.
problem Learning in infinite-horizon discounted decision processes with unknown parameters.
method Developed a general canonical probability space and new metrics for analyzing adaptive learning algorithms.
result Thompson Sampling achieves complete learning in complex decision-making problems.
New algorithms minimize regret in SSP with optimal sparse updates.
problem Minimizing regret in Stochastic Shortest Path models.
method Implicit finite-horizon approximation for analysis, model-free and model-based algorithms developed.
result Minimax optimal regret for both model-free and model-based algorithms.
Paper proposes an efficient online learning method using an offline dataset for infinite horizon MDPs.
problem Efficient online reinforcement learning in infinite horizon MDPs with an unknown expert policy.
method Bayesian approach to model the expert's policy and minimize cumulative regret.
result Upper bound on regret of i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) for the Informed PSRL algorithm. 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.
A new model-free algorithm achieves near-optimal regret for infinite-horizon MDPs.
problem Model-free reinforcement learning for infinite-horizon average-reward MDPs.
method Exploration Enhanced Q-learning (EE-QL) for weakly communicating MDPs.
result Achieves O ( T ) O(\sqrt{T}) O ( T ) regret bound for general weakly communicating MDPs. Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.
problem Optimizing control actions in unknown continuous-time systems over a finite time horizon.
method Least-squares algorithm based on continuous-time observations and controls, with perturbation analysis and parameter estimation error analysis.
result Logarithmic regret bound of order O ( ( ln M ) ( ln ln M ) ) O((\ln M)(\ln\ln M)) O (( ln M ) ( ln ln M )) . New algorithm tackles adversarial RL without horizon constraints.
problem Adversarial reinforcement learning with unknown transition kernel.
method Uses weighted least square estimator and occupancy measure for policy search.
result Achieves near-optimal regret bound of O ( K ) O(\sqrt{K}) O ( K ) . We establish that an optimistic variant of Q-learning applied to a fixed-horizon episodic Markov decision process with an aggregated state representation incurs regret O ~ ( H 5 M K + ε H K ) \tilde{\mathcal{O}}(\sqrt{H^5 M K} + εHK) O ~ ( H 5 M K + ε H K ) , where H H H is the horizon, M M M is the number of aggregate states, K K K is the number of episodes, and ε ε ε is …
New algorithms for learning MDPs with linear approximations in infinite-horizon settings.
problem Learning infinite-horizon average-reward MDPs with linear function approximation.
method Optimism principle, adversarial linear bandits, Natural Policy Gradient.
result Efficient algorithms with optimal or near-optimal regret bounds.
I analyse the frequentist regret of the famous Gittins index strategy for multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it turns out that this approach leads to finite-time regret guarantees comparable to those available for the popular UCB algorithm. Along the way I derive finite-time bounds…
New algorithms learn MDPs with better regret bounds using generative sampling.
problem Learning MDPs with optimal policies under uncertainty.
method Hybrid exploration-generative RL model, classical and quantum algorithms.
result Quantum algorithms achieve poly log T \operatorname{poly}\log{T} poly log T regret for infinite-horizon MDPs. Logarithmic regret for continuous-time reinforcement learning.
problem Continuous-time Markov decision processes with unknown transition probabilities and holding times.
method Upper confidence reinforcement learning, mean holding time estimation, stochastic comparison of point processes.
result Logarithmic regret bound achieved in finite time.
New RL method learns K-step lookahead Q-functions for fixed-horizon MDPs.
problem Challenges in online reinforcement learning for non-episodic, finite-horizon MDPs.
method Introduces a K-step lookahead Q-function with a time-varying threshold for selecting actions.
result Achieves minimax optimal constant regret for K=1 and O ( max ( ( K − 1 ) , C K − 1 ) S A T log ( T ) ) \mathcal{O}(\max((K-1),C_{K-1})\sqrt{SAT\log(T)}) O ( max (( K − 1 ) , C K − 1 ) S A T log ( T ) ) regret for K ≥ 2. New algorithm reduces regret in infinite MDPs with optimal variance-dependent bounds.
problem Infinite horizon MDPs lack optimal algorithms with low regret.
method Developed a UCB-style algorithm for average-reward and γ-regret.
result Achieved optimal variance-dependent regret bounds for both objectives.
New algorithm reduces regret in delayed feedback generalised linear bandits.
problem Regret in delayed feedback generalised linear bandits.
method Adaptation of optimistic algorithm to delayed feedback.
result Achieves a regret bound independent of the horizon's delay penalty.
New algorithms reduce contextual bandits' regret without knowing reward noise variances.
problem Reducing regret in contextual bandits with unknown reward noise variances.
method Developed new algorithms based on the optimism principle.
result Regret scales as the square root of the sum of measurement variances, not the time horizon.
Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-r…
UCRL2-VTR achieves nearly optimal regret for learning MDPs with linear function approximation.
problem Learning infinite-horizon average-reward MDPs with linear function approximation.
method UCRL2-VTR algorithm with Bernstein-type bonus.
result Achieves a regret of i l d e O ( d D T ) ilde{O}(d\sqrt{DT}) i l d e O ( d D T ) with matching lower bound. UCB-Advantage learns MDPs with O ( H 2 S A T ) O(\sqrt{H^2SAT}) O ( H 2 S A T ) regret.
problem Model-free reinforcement learning in finite-horizon MDPs.
method Reference-Advantage decomposition for low regret.
result Achieves i l d e O ( H 2 S A T ) ilde{O}(\sqrt{H^2SAT}) i l d e O ( H 2 S A T ) regret, matching best known bounds. New RL algorithm reduces regret in finite-horizon episodic tasks.
problem Minimizing regret in model-based reinforcement learning.
method Optimism principle applied to value-targeted regression.
result Regret bound of i l d e O ( d H 3 T ) ilde{\mathcal{O}}(d\sqrt{H^{3}T}) i l d e O ( d H 3 T ) for linear mixtures. Kernel-UCBVI algorithm balances exploration and exploitation in metric state-action spaces.
problem Exploration-exploitation dilemma in finite-horizon reinforcement learning with metric state-action spaces.
method Kernel-UCBVI, leveraging smoothness and kernel estimators of rewards and transitions.
result First regret bound for kernel-based RL using smoothing kernels, O ( H 3 K 2 d / ( 2 d + 1 ) ) O(H^3 K^{2d/(2d+1)}) O ( H 3 K 2 d / ( 2 d + 1 ) ) . Efficient RL for linear MDPs with unknown transitions.
problem Long planning horizons and unknown state transitions in linear mixture MDPs.
method Horizon-free algorithm using weighted least squares with variance and uncertainty awareness.
result Achieves optimal regret up to logarithmic factors.
Unified online tensor learning algorithm reduces computational and memory costs.
problem Efficiently learning from large tensors with minimal data storage and timely predictions.
method oRGrad algorithm for online tensor learning.
result oRGrad achieves optimal O ( T 1 / 2 ) O(T^{1/2}) O ( T 1/2 ) regret and O ( log T ) O(\log T) O ( log T ) adaptive regret. Optimal algorithm found for anytime regret with two experts.
problem Minimizing regret in prediction with two experts when time horizon is unknown.
method Designing a minimax optimal algorithm using ideas from stochastic calculus.
result Proved the optimal regret is γ√t / 2 for all time steps t.
In this paper, we consider the distributed stochastic multi-armed bandit problem, where a global arm set can be accessed by multiple players independently. The players are allowed to exchange their history of observations with each other at specific points in time. We study the relationship between regret and communica…
Paper improves worst-case regret bounds for RLSVI in reinforcement learning.
problem Minimizing regret in reinforcement learning with randomized value functions.
method Introduces a clipping variant of Thompson Sampling for RLSVI.
result Achieves a i l d e O ( H 2 S A T ) ilde{\mathrm{O}}(H^2S\sqrt{AT}) i l d e O ( H 2 S A T ) worst-case regret bound. New algorithm reduces regret in CMDPs without cancellation of errors.
problem Lagrangian approaches in CMDPs struggle with cancellation of errors.
method OptAug-CMDP, based on augmented Lagrangian method.
result Regret of i l d e O ( K ) ilde{O}(\sqrt{K}) i l d e O ( K ) for both objective and constraint violation. Study sparsity benefits in infinite feature contextual bandits.
problem Minimizing regret in infinite feature contextual bandits.
method Novel reduction to multi-armed bandits, Feel-Good Thompson Sampling algorithm.
result Regret bounds match lower bounds up to logarithmic factors, logarithmic dependence on effective features.
I introduce and analyse an anytime version of the Optimally Confident UCB (OCUCB) algorithm designed for minimising the cumulative regret in finite-armed stochastic bandits with subgaussian noise. The new algorithm is simple, intuitive (in hindsight) and comes with the strongest finite-time regret guarantees for a hori…
Memory-limited learning tackles adversarial bandits with reduced storage.
problem Adversarial bandit problem with limited memory storage.
method Hierarchical learning policy with sublinear memory requirement.
result Established sublinear regret bounds for weak and shifting regrets.
Study optimal policy regret in partially observable Markov games with adaptive opponents.
problem Optimal sequential decision-making in partially observable environments against strategic, adaptive opponents.
method An epoch-based optimistic maximum-likelihood algorithm that selects one policy per epoch using confidence sets built cumulatively from past data.
result Achieves i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) policy regret for fixed problem parameters, with explicit dependence on horizon, adversary memory, confidence radius, and aggregate Eluder dimension. We study optimal regret bounds for control in linear dynamical systems under adversarially changing strongly convex cost functions, given the knowledge of transition dynamics. This includes several well studied and fundamental frameworks such as the Kalman filter and the linear quadratic regulator. State of the art met…
New algorithm tackles smooth online learning with optimal regret.
problem Smoothed online learning with adversarial distributions.
method Oracle-efficient algorithms for nonparametric function classes.
result Oracle-efficient algorithms achieve optimal regret bounds.
Algorithm minimizes regret in multi-criteria bandits with constraints.
problem Optimize primary attribute while respecting secondary constraints.
method Con-LCB algorithm that guarantees logarithmic regret and feasibility identification.
result Logarithmic regret and feasibility identification with high probability.
In online learning, the dynamic regret metric chooses the reference (optimal) solution that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The dynamic regret metric is particularly interesting for applications such as online reco…
We consider the problem of learning in episodic finite-horizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses. We propose an efficient algorithm that achieves O ~ ( L ∣ X ∣ ∣ A ∣ T ) \mathcal{\tilde{O}}(L|X|\sqrt{|A|T}) O ~ ( L ∣ X ∣ ∣ A ∣ T ) regret with high probability, where L L L is the horizon, ∣ X ∣ |X| ∣ X ∣ is t…
We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning (RL). When the state space is large or continuous, traditional tabular approaches are unfeasible and some form of function approximation is mandatory. In this paper, we introduce an optimistically-initialized variant of the popula…
New algorithms reduce matching regret by limiting frequent updates.
problem Minimizing regret in stochastic matching with rare optimization updates.
method Batched algorithms that limit matching updates to Θ(log log T) rounds.
result Achieve a regret bound of \(\widetilde{\mathcal{O}}(\sqrt{T})\) with reduced computational cost.
New algorithm reduces reinforcement learning regret to sqrt(T) without strong dynamics assumptions.
problem Infinite-horizon average-reward reinforcement learning with linear MDPs.
method Approximate by discounted-reward MDPs and apply optimistic value iteration.
result Achieves O(sqrt(T)) regret with polynomial complexity.
In this short note we consider a dynamic assortment planning problem under the capacitated multinomial logit (MNL) bandit model. We prove a tight lower bound on the accumulated regret that matches existing regret upper bounds for all parameters (time horizon T T T , number of items N N N and maximum assortment capacity K K K )…
New algorithms reduce slate bandit regret for large slates, outperforming existing methods.
problem Non-separable reward functions in slate bandits with many slates.
method Design of algorithms with sub-linear regret.
result Sub-linear regret with respect to the time horizon for large number of slates.
Algorithm reduces long-term policy regret in ML decision-making.
problem Capturing long-term impacts of ML decisions in communities.
method Modeling communities as arms in a multi-armed bandit problem, defining policy regret as a stronger metric than external regret.
result Algorithm achieves provably sub-linear policy regret for long time horizons.
UCRL-CMDP algorithm optimizes RL with constraints on average costs.
problem Optimizing RL in MDPs with average cost constraints.
method Model-based RL algorithms maximizing reward while keeping costs within bounds.
result UCRL-CMDP algorithm's expected regret is upper-bounded by $T^{2\slash 3}$ .
Algorithm reduces regret in partially observable systems by learning dynamics and using optimistic control.
problem Minimizing regret in partially observable linear quadratic control systems with unknown dynamics.
method ExpCommit algorithm that learns model parameters and uses optimism in uncertainty.
result End-to-end sublinear regret upper bound of O ~ ( T 2 / 3 ) \tilde{\mathcal{O}}(T^{2/3}) O ~ ( T 2/3 ) for ExpCommit. Optimal switching regret for all segmentations in online convex optimisation.
problem Non-stationary online convex optimisation problems.
method Developed an efficient algorithm to achieve optimal switching regret on every possible segmentation.
result Achieved asymptotically optimal switching regret on every possible segmentation simultaneously.