Policy gradient methods achieve linear convergence in simple MDPs.
problem Analyzing convergence rates of policy gradient methods in finite MDPs.
method Connections with policy iteration to show linear convergence with large step-sizes.
result Policy gradient methods succeed with large step-sizes and achieve linear rate of convergence.
The paper analyzes the sample complexities for policy evaluation with linear function approximation.
problem Policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes.
method Investigates sample complexities for two policy evaluation algorithms: TD and TDC.
result Establishes high-probability sample complexity bounds for policy evaluation algorithms.
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.
problem System identification for linear systems with nonlinear and/or time-varying policies under i.i.d. random excitation noises.
method Least square estimation with non-asymptotic error bound for bounded state and action trajectories.
result The error bound is consistent with linear policies and generalizes existing guarantees.
Presents SPEED, an algorithm for optimal policy evaluation in linear bandits with heteroscedastic noise.
problem Optimal data collection for policy evaluation in linear bandits with heteroscedastic reward noise.
method Formulated an optimal design for weighted least squares estimates, derived the optimal sample allocation, introduced SPEED algorithm, and derived regret bounds.
result SPEED leads to policy evaluation with MSE comparable to oracle strategy and significantly lower than random policy execution.
Optimistic actor-critic tackles linear MDPs with parametric policies.
problem Theoretical limitations of existing actor-critic methods for linear MDPs.
method Proposes an optimistic actor-critic framework with parametric log-linear policies and approximate Thompson sampling.
result Achieves state-of-the-art sample complexity in both on-policy and off-policy settings.
ENIAC method optimizes and explores complex RL problems with non-linear policies.
problem Theoretical understanding of non-linear policies in RL with strategic exploration.
method ENIAC, an actor-critic method for non-linear function approximation.
result ENIAC finds near-optimal policies in polynomial exploration rounds under bounded eluder dimension.
Designs a single policy for collecting data to train near-optimal policies.
problem Engineering overhead in deploying minimax procedures for stochastic linear contextual bandits.
method Designs a single stochastic policy to collect data from which a near-optimal policy can be extracted.
result The designed policy can collect data from which a near-optimal policy can be extracted.
Learning the value function of a given policy (target policy) from the data samples obtained from a different policy (behavior policy) is an important problem in Reinforcement Learning (RL). This problem is studied under the setting of off-policy prediction. Temporal Difference (TD) learning algorithms are a popular cl…
Policy gradient converges linearly with Hadamard parameterization in tabular settings.
problem Convergence of policy gradient methods under Hadamard parameterization.
method Studied convergence rate and established linear convergence after k 0 k_0 k 0 iterations. result Algorithm converges linearly with rate $O( rac{1}{k})$ and faster locally after k 0 k_0 k 0 . VA-OPE improves OPE by incorporating variance information, achieving tighter error bounds.
problem Estimating value function of a target policy from offline data collected by a behavior policy.
method Proposes VA-OPE, an algorithm that reweights Bellman residual using estimated variance of the value function.
result Achieves a tighter error bound than the best-known result.
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.
New method for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.
This work characterizes conditions for offline policy evaluation in reinforcement learning.
problem Understanding when classical methods succeed in offline policy evaluation for linear function approximation.
method Control-theoretic and linear-algebraic conditions for classical methods (FQI and LSTD).
result A precise hierarchy of regimes under which these estimators succeed, and a complete picture of their behavior.
FLAP adapts policies quickly to new tasks using shared linear representations.
problem Adapting policies to new tasks efficiently and effectively.
method FLAP uses a shared linear representation and a separate adapter network for quick adaptation.
result FLAP achieves up to 8X faster adaptation and significantly better performance on out-of-distribution tasks.
Novel framework for policy optimization with general parameterization and linear convergence.
problem Lack of theoretical guarantees for policy optimization with general parameterization schemes.
method Mirror descent approach for policy optimization with general parameterization.
result First result of linear convergence for policy-gradient-based method with general parameterization.
Greedy policy maximizes information in unknown linear systems.
problem Exploration in unknown linear dynamical systems.
method Online greedy policy maximizing information.
result Competitive performance compared to gradient-based methods.
Off-policy reinforcement learning has many applications including: learning from demonstration, learning multiple goal seeking policies in parallel, and representing predictive knowledge. Recently there has been an proliferation of new policy-evaluation algorithms that fill a longstanding algorithmic void in reinforcem…
PROPO tackles non-stationary MDPs with efficient policy optimization.
problem Non-stationary MDPs with varying reward and transition kernels.
method PROPO, a periodic restarted optimistic policy optimization algorithm with sliding-window-based policy evaluation and improvement.
result PROPO achieves near-optimal performance in non-stationary MDPs.
GPMD solves regularized RL with linear convergence, promoting structural policies.
problem Regularized reinforcement learning to encourage exploration and structural policies.
method Policy mirror descent with generalized convex regularizers and Bregman divergence.
result GPMD converges linearly to the global solution over a wide range of learning rates.
Extends double linear policy with time-varying weights and proves robust positive expectation.
problem Ensuring robustness in policy optimization with time-varying parameters.
method Employed a novel elementary symmetric polynomials characterization approach to prove robust positive expectation (RPE). Derived explicit expressions for expected cumulative gain-loss and variance.
result Proved the robust positive expectation property holds for the extended double linear policy.
Study policy gradient for large-agent mean-field control and game in continuous time.
problem Optimal policy learning for large number of agents in continuous-time mean-field systems.
method Policy gradient method applied to linear-quadratic mean-field control and game models.
result Policy gradient converges to optimal solution at a linear rate for both mean-field control and game.
A single policy suffices for near-optimal parallel exploration in RL.
problem Quantitative effects of parallel exploration in reward-free RL.
method Using a single policy to guide exploration across all agents.
result Near-linear speedup and near-minimax optimality for linear MDPs.
Paper studies offline RL with linear approx, focusing on inherent Bellman error.
problem Offline RL with linear approx, focusing on inherent Bellman error.
method Algorithm that succeeds under single-policy coverage condition, leveraging inherent Bellman error.
result Algorithm yields first known guarantee under single-policy coverage, even for linear Bellman completeness.
RL solves discrete LQ control with Gaussian optimal policy.
problem Discrete-time linear-quadratic control problem.
method Entropy-based RL to find Gaussian optimal policy.
result RL algorithm solves mean-variance asset-liability management problem.
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.
Study agnostic feature-based dynamic pricing models with linear policies and noisy valuations.
problem Tackles dynamic pricing with unknown noise and no assumptions on data.
method Studies two agnostic models: linear policy and linear noisy valuation, presenting algorithms and regret bounds.
result Demonstrates no-regret learning is possible under weak assumptions, but noisy feedback is not significantly more useful than bandit feedback.
Entropy-regularized NPG converges linearly with linear function approximation.
problem Analyzing convergence of entropy-regularized NPG with function approximation.
method Established finite-time convergence analyses with entropy regularization and linear function approximation.
result Entropy-regularized NPG achieves linear convergence up to a function approximation error.
Efficient RL algorithm for MDPs with linear Q π Q^π Q π realizability, achieving optimal regret bound.
problem Efficient reinforcement learning under linear Q π Q^π Q π realizability assumption for MDPs with stochastic dynamics. method Frozen Policy Iteration algorithm that uses high-confidence data and freezes policy for well-explored states.
result Achieves optimal regret bound of O ~ ( d 2 H 6 T ) \widetilde{O}(\sqrt{d^2H^6T}) O ( d 2 H 6 T ) for linear (contextual) bandits. New algorithms identify best policies in discounted linear MDPs efficiently.
problem Identifying the best policy in discounted linear MDPs with limited samples.
method Derive lower bounds and devise simple yet near-optimal algorithms.
result Upper bound on sample complexity matches existing bounds.
Policy gradient methods find Nash equilibrium in noisy games.
problem Finding Nash equilibrium in noisy games.
method Policy gradient methods with noise added.
result Policy gradient methods converge to Nash equilibrium in noisy games.
Study on PG learning for LQ MFC problems with common noise, proving convergence and sample complexity.
problem Optimal policy learning in LQ MFC problems with common noise and entropy regularization.
method Comprehensive error analysis of PG algorithms in both model-based and model-free settings.
result Global linear convergence and sample complexity of PG algorithms in model-free setting.
This paper studies GAIL's global convergence for general MDP and nonlinear rewards.
problem Understanding when GAIL algorithms achieve global convergence for general MDP and nonlinear rewards.
method Characterization of global convergence for various policy gradient algorithms applied to GAIL.
result First systematic theoretical study of GAIL for global convergence.
Efficient local planning with linear approximations for agents with limited simulator access.
problem Planning with limited simulator access in reinforcement learning.
method Confident Monte Carlo Least Square Policy Iteration (Confident MC-LSPI) and Politex (Confident MC-Politex) algorithms.
result The algorithms can learn the optimal policy with local simulator access, even for linear Q-functions.
Excessively changing policies in many real world scenarios is difficult, unethical, or expensive. After all, doctor guidelines, tax codes, and price lists can only be reprinted so often. We may thus want to only change a policy when it is probable that the change is beneficial. In cases that a policy is a threshold on …
Policy gradient methods converge for LQR problems with noisy state dynamics.
problem Finding optimal policies in noisy LQR problems over finite time horizons.
method Policy gradient methods with convergence guarantees for finite time and stochastic state dynamics.
result Global linear convergence for policy gradient methods in LQR problems with weak assumptions.
New method efficiently evaluates policies using trajectory data.
problem Statistically efficient policy evaluation with limited data.
method Trajectory-based approach for policy evaluation.
result Improved sample complexity for policy evaluation.
DR-RPO optimizes robust policies in RL with limited interaction, achieving sublinear regret.
problem Policy optimization in RL under distribution shift and adversarial dynamics.
method DR-RPO algorithm incorporating reference-policy regularization and upper confidence bonus for exploration.
result DR-RPO achieves sublinear regret and polynomial suboptimality bounds in robust RL.
We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconve…
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 i l d e O ( d 3 / 4 H 2 K 3 / 4 ) ilde{\mathcal{O}}(d^{3/4}H^2K^{3/4}) i l d e O ( d 3/4 H 2 K 3/4 ) regret bound. Optimistic NPG improves policy optimization in online RL with efficient sample complexity.
problem Limited theoretical understanding of policy optimization, especially in online RL.
method Combines natural policy gradient with optimistic policy evaluation.
result Achieves optimal dimension dependence sample complexity for learning near-optimal policies.
Adapts model-based advice to stabilize black-box policies for nonlinear control.
problem Stabilizing machine-learned policies for nonlinear control with limited model information.
method Proposes an adaptive λ λ λ -confident policy to combine black-box and model-based advice. result Proves the stability of the adaptive λ λ λ -confident policy and its competitive ratio. We analyze the problem of learning a single user's preferences in an active learning setting, sequentially and adaptively querying the user over a finite time horizon. Learning is conducted via choice-based queries, where the user selects her preferred option among a small subset of offered alternatives. These queries …
Oracle-efficient algorithm for offline RL with partial data coverage.
problem Offline reinforcement learning with partial data coverage and constraints.
method PDOCRL, a primal-dual algorithm with decomposed linear-programming formulation.
result Near-optimal, near-feasible policy with \(\widetilde{\mathcal O}(ε^{-2})\) sample guarantee.
This work develops a fully decentralized multi-agent algorithm for policy evaluation. The proposed scheme can be applied to two distinct scenarios. In the first scenario, a collection of agents have distinct datasets gathered following different behavior policies (none of which is required to explore the full state spa…
Linear Q-learning converges to a bounded set without divergence.
problem Proving linear Q-learning does not diverge and converges to a bounded set.
method No modifications to the original linear Q-learning algorithm, no Bellman completeness or near-optimality assumptions, only an ε-softmax behavior policy with adaptive temperature.
result First L 2 L^2 L 2 convergence rate of linear Q-learning iterates to a bounded set. BCRL learns a Bellman complete representation for offline RL policy evaluation.
problem Learning a Q-function efficiently from offline data.
method BCRL learns a linear Bellman complete representation directly from data, enabling efficient OPE.
result BCRL achieves competitive OPE error and outperforms FQE in certain scenarios.
Policy evaluation is a crucial step in many reinforcement-learning procedures, which estimates a value function that predicts states' long-term value under a given policy. In this paper, we focus on policy evaluation with linear function approximation over a fixed dataset. We first transform the empirical policy evalua…