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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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13253850 · Jun 202019922001200920172026
48 results for Episodic MDP

We consider online learning in episodic loop-free Markov decision processes (MDPs), where the loss function can change arbitrarily between episodes, and the transition function is not known to the learner. We show O~(LXAT)\tilde{O}(L|X|\sqrt{|A|T}) regret bound, where TT is the number of episodes, XX is the state space, $A…

2019-05-19abs ↗pdf ↗

We consider a reinforcement learning (RL) setting in which the agent interacts with a sequence of episodic MDPs. At the start of each episode the agent has access to some side-information or context that determines the dynamics of the MDP for that episode. Our setting is motivated by applications in healthcare where ba…

2017-11-15abs ↗pdf ↗

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…

2019-05-09abs ↗pdf ↗

Improved regret bound for MNL MDPs with variance-aware approach.

problem Optimal reinforcement learning for MNL MDPs with structured variance.
method Introducing a problem-dependent constant measuring average variance, proposing an algorithm with improved regret bound.
result Minimax optimal regret bound of O(dH2σˉTT)O(dH^2\barσ_T\sqrt{T}) for structured MDPs.

Optimistic PPO variant solves linear MDPs with improved regret bound.

problem Understanding theoretical limits of PPO in linear MDPs.
method Proposes an optimistic variant of PPO for episodic adversarial linear MDPs with full-information feedback.
result Establishes a ildeO(d3/4H2K3/4) ilde{\mathcal{O}}(d^{3/4}H^2K^{3/4}) regret bound.

Algorithm for online learning in MDPs with linear function approximation and bandit feedback.

problem Online learning in MDPs with changing reward functions and limited feedback.
method Developed MDP-LinExp3 algorithm with theoretical guarantees.
result Proved regret bounds for MDP-LinExp3 algorithm.

New framework for reinforcement learning with adversarial preferences in tabular MDPs.

problem Learning from preferences rather than direct rewards in MDPs with adversarial settings.
method Developed PbMDPs framework, established lower bounds, and proposed algorithms for regret minimization.
result Achieved regret bounds of Ω((H2SK)1/3T2/3)Ω( (H^2 S K)^{1/3} T^{2/3} ) for PbMDPs with Borda scores.

New algorithms reduce reinforcement learning regret in factored MDPs.

problem Optimizing reinforcement learning in non-episodic factored MDPs.
method Proposed two near-optimal and oracle-efficient algorithms for FMDPs.
result Oracle-efficient algorithms achieve near-optimal regret bounds of O(DSAT)O(DS\sqrt{AT}).

Algorithm learns both stochastic and adversarial MDPs with best-of-both-worlds guarantees.

problem Learning episodic MDPs with known transition and bandit feedback.
method Follow-the-Regularized-Leader method with a hybrid regularizer.
result Achieves O(logT)\mathcal{O}(log T) regret for stochastic losses and ildeO(T) ilde{\mathcal{O}}(\sqrt{T}) regret for adversarial losses.

Study online learning in MDPs with aggregate bandit feedback, achieving low regret in both stochastic and adversarial settings.

problem Online learning in finite-horizon episodic MDPs with aggregate bandit feedback.
method Best-of-both-worlds (BOBW) algorithms using FTRL over occupancy measures, self-bounding techniques, and new loss estimators.
result First BOBW algorithms for episodic tabular MDPs with aggregate bandit feedback achieving O(logT)O(\log T) regret in stochastic and O(T){O}(\sqrt{T}) regret in adversarial settings.

New RL algorithm achieves nearly optimal performance for linear MDPs.

problem Optimal reinforcement learning for episodic linear MDPs.
method Weighted linear regression with variance estimator and rare-switching policy.
result Achieves nearly minimax optimal regret ildeO(dH3K) ilde O(d\sqrt{H^3K}).

Paper explores limits of imitation learning in MDPs, setting new suboptimality bounds.

problem Understanding the statistical limits of imitation learning in MDPs.
method Analyzes minimax statistical limits in two settings: pre-interaction and interaction.
result Establishes suboptimality bounds for imitation learning in MDPs, showing improvements with knowledge of transition.

Algorithm learns near-optimal policies for reward-mixing MDPs with few latent contexts.

problem Episodic reinforcement learning in reward-mixing Markov decision processes with a few latent contexts.
method Sample-efficient algorithm EM^2 using higher-order method-of-moments approach.
result Provides an ε-optimal policy using O(ε^(-2) * S^d A^d * poly(H, Z)^d) episodes for arbitrary M ≥ 2.

Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for ex…

2015-10-29abs ↗pdf ↗

KeRNS tackles non-stationary reinforcement learning in metric spaces.

problem Non-stationary reinforcement learning in metric spaces.
method KeRNS uses time-dependent kernels to model non-stationary Markov Decision Processes (MDPs).
result KeRNS achieves a regret bound that scales with the covering dimension and total variation of the MDP.

Paper bounds PAC RL sample complexity in deterministic MDPs.

problem Identify ε-optimal policy with high probability.
method Proposes nearly matching upper and lower bounds on sample complexity, introduces deterministic return gap, uses graph-theoretical concepts and maximum-coverage exploration.
result First nearly matching upper and lower bounds on sample complexity for PAC RL in deterministic MDPs.

We study online learning of finite Markov decision process (MDP) problems when a side information vector is available. The problem is motivated by applications such as clinical trials, recommendation systems, etc. Such applications have an episodic structure, where each episode corresponds to a patient/customer. Our ob…

2014-06-26abs ↗pdf ↗

Paper establishes first instance-dependent lower bound for PAC reinforcement learning.

problem Identifying near-optimal policies in tabular MDPs with minimal samples.
method Proposes instance-dependent lower bound for sample complexity.
result Lower bound closely matches PEDEL algorithm's sample complexity.

New method achieves nearly horizon-free offline reinforcement learning for tabular and linear MDPs.

problem Achieving efficient reinforcement learning without knowing the horizon.
method Simple recursion-based method to bound total variance in offline scenarios.
result Nearly horizon-free sample complexity bounds for offline policy evaluation and optimization.

New algorithms reduce regret in online MDPs by adapting to data and variance.

problem Adapting to both adversarial and stochastic environments in online MDPs.
method Develops algorithms based on global optimization and policy optimization, using optimistic follow-the-regularized-leader with log-barrier regularization.
result Achieves refined data-dependent and variance-dependent regret bounds.

New algorithm learns optimal policies with just 1 episode, settling horizon-dependence in RL.

problem Understanding the sample complexity of reinforcement learning with horizon length.
method Developed an algorithm using only O(1)O(1) episodes to achieve PAC guarantee, leveraging connections between value functions in discounted and finite-horizon MDPs and novel perturbation analysis.
result Achieved the same PAC guarantee with only O(1)O(1) episodes of environment interactions, completely settling horizon-dependence in RL.

Efficiently identifies best policies in tabular MDPs with reduced computational cost.

problem Identifying the best policy in tabular MDPs with high computational cost.
method Combines posterior sampling with online learning to achieve asymptotic optimality.
result Achieves optimal sample complexity and posterior contraction rate with O(S2AH)O(S^2AH) per episode.

Efficient RL algorithm for multinomial logistic MDPs with provable guarantees.

problem Model-based RL for episodic MDPs with unknown transition probabilities.
method Upper confidence bound-based algorithm for exploration-exploitation balance.
result Achieves ildeO(dH3T) ilde{O}(d \sqrt{H^3 T}) regret bound for multinomial logistic models.

Quantum UCB algorithm reduces reinforcement learning regret exponentially.

problem Episodic reinforcement learning with quantum state evolution.
method Upper Confidence Bound (UCB) quantum algorithm with quantum mean estimation.
result Exponential improvement in regret from $\Tilde{\mathcal{O}}(\sqrt{K})$ to $\Tilde{\mathcal{O}}(1)$.

New algorithm reduces dynamic regret for MDPs with unknown transition and adversarial rewards.

problem Episodic linear mixture MDPs with unknown transition and adversarial rewards.
method Combines occupancy-measure-based global optimization and policy-based variance-aware value-targeted regression.
result Achieves near-optimal dynamic regret of O~(dH3K+HK(H+PˉK))\widetilde{\mathcal{O}}(d \sqrt{H^3 K} + \sqrt{HK(H + \bar{P}_K)}).

We consider the recently proposed reinforcement learning (RL) framework of Contextual Markov Decision Processes (CMDP), where the agent interacts with a (potentially adversarial) sequence of episodic tabular MDPs. In addition, a context vector determining the MDP parameters is available to the agent at the start of eac…

2019-03-14abs ↗pdf ↗

New algorithm reduces reinforcement learning regret for linear MDPs with unknown transitions.

problem Adversarial linear mixture MDPs with bandit feedback and unknown transition.
method Proposes a new algorithm with a least square estimator and self-normalized concentration.
result Achieves improved regret bound with high probability.

Optimistic algorithm reduces regret in non-stationary linear MDPs.

problem Efficient learning in non-stationary linear MDPs with evolving reward and transition.
method OPT-WLSVI, an optimistic model-free algorithm using exponential weights.
result Achieves a regret bound of O~(d5/4H2Δ1/4K3/4)\widetilde{\mathcal{O}}(d^{5/4}H^2 Δ^{1/4} K^{3/4}).

This is a brief technical note to clarify some of the issues with applying the application of the algorithm posterior sampling for reinforcement learning (PSRL) in environments without fixed episodes. In particular, this paper aims to: - Review some of results which have been proven for finite horizon MDPs (Osband et a…

2016-08-09abs ↗pdf ↗

We take initial steps in studying PAC-MDP algorithms with limited adaptivity, that is, algorithms that change its exploration policy as infrequently as possible during regret minimization. This is motivated by the difficulty of running fully adaptive algorithms in real-world applications (such as medical domains), and …

2019-05-30abs ↗pdf ↗

The paper proves almost sure convergence of MCES algorithm for a specific class of MDPs.

problem Establishing convergence for the Monte Carlo Exploring Starts (MCES) algorithm in reinforcement learning.
method Introduced a novel inductive approach based on the strong law of large numbers.
result Almost sure convergence for Optimal Policy Feed-Forward MDPs.

In an episodic Markov Decision Process (MDP) problem, an online algorithm chooses from a set of actions in a sequence of HH trials, where HH is the episode length, in order to maximize the total payoff of the chosen actions. Q-learning, as the most popular model-free reinforcement learning (RL) algorithm, directly pa…

2019-04-24abs ↗pdf ↗

Safe reinforcement learning tackles safety constraints with linear approximations.

problem Ensuring safety in reinforcement learning without violating constraints.
method Modeling safety as a linear cost function, developing SLUCB-QVI and RSLUCB-QVI algorithms for MDPs with linear function approximation.
result Achieved a nearly optimal regret bound for safe reinforcement learning, matching state-of-the-art unsafe algorithms.