New method stabilizes FQE by reweighting Bellman targets.
problem Stability guarantees for FQE often rely on Bellman completeness, which can fail with function approximation.
method Proposes stationary-weighted FQE, reweighting Bellman targets by stationary target-to-behavior density ratio.
result Proves finite-sample linear convergence to stationary projected Bellman fixed point without Bellman completeness.
DSPI connects natural policy gradient to policy iteration, proving global convergence.
problem Optimizing policies in reinforcement learning.
method DSPI framework, combining smoothed policy iteration and natural policy gradient.
result DSPI achieves geometric convergence and optimal complexity for policy optimization.
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.
New Bellman error estimator improves offline model selection performance.
problem Selecting the best policy from logged data using mean squared Bellman error.
method Developed a more accurate estimator of MSBE and analyzed conditions for successful OMS.
result New estimator achieves impressive offline model selection performance on diverse tasks.
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.
The paper analyzes off-policy TD-learning using generalized Bellman operators and provides finite-sample bounds.
problem High variance in off-policy TD-learning due to importance sampling.
method Derives finite-sample bounds for off-policy TD-like algorithms using generalized Bellman operators.
result First-known finite-sample guarantees for several off-policy TD algorithms.
New method for distributional off-policy evaluation using Bellman residual minimization.
problem Learning return distribution from offline data generated by a different policy.
method Energy Bellman Residual Minimizer (EBRM) method.
result Established finite-sample error bound for EBRM estimator.
The paper explores solutions to the distributional Bellman equation in reinforcement learning.
problem Distributional reinforcement learning considers complete return distributions, not just expected returns.
method Study existence and uniqueness of solutions to general distributional Bellman equations, linking them to multivariate affine equations.
result Any solution to a distributional Bellman equation can be derived from a multivariate affine distributional equation.
New method improves stability of soft FQI for offline RL.
problem Stability issues in soft FQI under function approximation.
method Stationary reweighting to align operator norms.
result Local linear convergence proved under certain conditions.
This paper aims at theoretically and empirically comparing two standard optimization criteria for Reinforcement Learning: i) maximization of the mean value and ii) minimization of the Bellman residual. For that purpose, we place ourselves in the framework of policy search algorithms, that are usually designed to maximi…
We propose a new objective function for finite-horizon episodic Markov decision processes that better captures Bellman's principle of optimality, and provide an expression for the gradient of the objective.
New method for rigorous confidence intervals in off-policy evaluation.
problem Evaluate new policies from off-policy data without executing them.
method Variational framework using kernel Bellman loss.
result Efficient method for tight confidence intervals in various settings.
New method for off-policy evaluation in POMDPs using future-dependent value functions.
problem Curse of horizon in off-policy evaluation for POMDPs.
method Develops future-dependent value functions and minimax learning method.
result PAC result and Bellman completeness for the proposed OPE estimator.
Direct and indirect RL methods classified and compared.
problem Classifying RL methods for sequential decision making.
method Direct RL solves optimal policy directly, indirect RL solves Bellman equation.
result Direct and indirect RL methods are equivalent and can be unified.
Selective state-adaptive regularization improves offline RL performance.
problem Extrapolation errors and value overestimation in static dataset RL.
method State-adaptive regularization coefficients trust Bellman-driven results selectively.
result Significant improvement in performance on D4RL benchmark.
Study risk-sensitive market making with entropy regularization for better quote control.
problem Risk-sensitive market making with exponential utility and penalties.
method Entropy-regularized certainty-equivalent Bellman policies for discrete-time market dynamics.
result Proves convergence and performance bounds for entropy-regularized policies.
Market makers optimize trading with a new implicit scheme for complex inequalities.
problem Optimizing trading in a limit order book with stochastic and impulse control.
method Implicit numerical scheme coupled with policy iteration algorithm.
result Convergence to the unique viscosity solution of the HJBQVI.
Second-order estimator improves continuous-time policy evaluation.
problem Estimating value surfaces from discrete data with time-inhomogeneous dynamics.
method Moment-matching coefficients for high-order generator regression.
result Second-order estimator consistently outperforms Bellman baseline.
Maximum entropy deep reinforcement learning (RL) methods have been demonstrated on a range of challenging continuous tasks. However, existing methods either suffer from severe instability when training on large off-policy data or cannot scale to tasks with very high state and action dimensionality such as 3D humanoid l…
KBB algorithm reduces sample complexity for policy evaluation in general state spaces.
problem Policy evaluation in large state spaces with high sample complexity.
method Alternates between fitting Bellman residual and estimating value function via adaptive feature set growth.
result Super-linear convergence rates demonstrated, with reductions in sample complexity.
A new method calibrates value predictions in offline RL to improve reliability.
problem Difficulty in long-horizon value prediction in offline reinforcement learning.
method Bellman calibration, a weak reliability criterion, and Iterated Bellman Calibration.
result Finite-sample guarantees show that Bellman calibration error is controlled at nonparametric rates.
This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) semi-Lagrangian discretization schemes applied to the HJBQVI proble…
FORE evaluates occupancy ratios without requiring Bellman completeness.
problem Offline reinforcement learning occupancy ratio estimation.
method Fitted occupancy-ratio evaluation (FORE) using adjoint Bellman recursion.
result FORE achieves convergence in KL without Bellman completeness.
The paper studies risk-sensitive MDPs with recursive risk measures.
problem Risk-sensitive decision-making in MDPs with unbounded costs.
method Recursive application of static risk measures, Bellman equation derivation, existence of optimal policies.
result Existence of Markovian optimal policies for infinite planning horizons, contractive model for stationary optimal policy.
We consider the exploration/exploitation problem in reinforcement learning. For exploitation, it is well known that the Bellman equation connects the value at any time-step to the expected value at subsequent time-steps. In this paper we consider a similar \textit{uncertainty} Bellman equation (UBE), which connects the…
Sequential decision making in the presence of uncertainty and stochastic dynamics gives rise to distributions over state/action trajectories in reinforcement learning (RL) and optimal control problems. This observation has led to a variety of connections between RL and inference in probabilistic graphical models (PGMs)…
New methods for off-policy evaluation in reinforcement learning.
problem Improving off-policy evaluation in reinforcement learning.
method Developed MWL and MQL estimators for importance weights and value functions.
result MWL and MQL provide a unified view of algorithms in reinforcement learning.
Paper solves Bayesian bandit problem with continuous-time limit and approximate policy.
problem Finding optimal policy in Bayesian bandit problems with large horizons.
method Reformulates Bayesian bandit problem as continuous Hamilton-Jacobi-Bellman (HJB) equation and proposes approximate Bayes-optimal policy.
result Approximate Bayes-optimal policy for large horizons with constant computational cost.
Develops a reinforcement learning algorithm for learning deterministic equilibrium policies in time-inconsistent control problems.
problem Learning equilibrium policies in time-inconsistent control problems.
method Continuous-time model-free reinforcement learning algorithm using deterministic policy gradient approach.
result Learned equilibrium policies in general time-inconsistent control problems.
A new method improves policy evaluation in RL by tracking value uncertainties.
problem Limitations in existing policy evaluation methods for deep RL tasks.
method KOVA (Kalman Optimization for Value Approximation) based on extended Kalman filter.
result KOVA minimizes a regularized objective function that considers parameter and noisy return uncertainties.
Polynomial-time RL algorithm for constant actions under linear Bellman completeness.
problem Efficient online reinforcement learning with few actions.
method Polynomial-time algorithm based on linear function approximation.
result First computationally efficient algorithm for RL with constant actions under linear Bellman completeness.
The impact of softmax on the value function itself in reinforcement learning (RL) is often viewed as problematic because it leads to sub-optimal value (or Q) functions and interferes with the contraction properties of the Bellman operator. Surprisingly, despite these concerns, and independent of its effect on explorati…
New approach uses PDE learning for faster RL fine-tuning.
problem Learning optimal control policy for diffusion process.
method Solves variational inequality based on HJB equations.
result Shows fine-tuning can be done via supervised regression.
The paper develops RL methods for optimal switching between multiple states.
problem Optimal switching between multiple states in continuous time.
method Entropy-regularized exploration, HJB equations, policy improvement, value function convergence.
result The RL algorithm converges to optimal policies as temperature parameter vanishes.
New RL approach infers optimal policies via variational inference.
problem Manual design of reward functions for reinforcement learning.
method Variational inference for inferring policies achieving desired outcomes.
result Eliminates need for hand-crafted reward functions for diverse tasks.
New algorithm for risk-sensitive reinforcement learning with natural policy gradients.
problem Risk-sensitive reinforcement learning with downside risk constraints.
method Introduce a new Bellman equation to estimate the lower partial moment of returns, use natural policy gradients, and extend Reward Constrained Policy Optimization.
result Sample-efficient estimation of partial moments and effective risk-sensitive control.
New algorithms solve robust MDPs efficiently, significantly faster than existing methods.
problem Computing robust MDP solutions with uncertainty in transition probabilities is computationally expensive.
method Partial policy iteration and fast robust Bellman operator computation methods.
result The proposed methods are many orders of magnitude faster than state-of-the-art approaches.
This work develops confidence intervals for off-policy evaluation.
problem Estimating expected reward with uncertainty quantification.
method Primal-dual optimization with kernel Bellman loss and martingale concentration inequality.
result Developed practical algorithm for non-asymptotic confidence intervals.
Paper shows equivalence between two dividend preference models.
problem Understanding investor and firm preferences for dividends.
method Formulated Epstein-Zin preference, proved equivalence with Maenhout's model.
result Robust dividend policy is equivalent to a threshold strategy based on surplus process.
The paper introduces Bellman-consistent pessimism to improve offline reinforcement learning without overly pessimistic bias.
problem Offline reinforcement learning's challenge of discovering good policies without exhaustive exploration.
method Introduces Bellman-consistent pessimism for function approximation, improving sample complexity and adaptability.
result Improves sample complexity by O ( d ) \mathcal{O}(d) O ( d ) in the action space finite case, and automatically adapts to bias-variance tradeoff. Paper introduces RCaI, a risk-sensitive control method using Rényi divergence.
problem Risk-sensitive control in reinforcement learning.
method RCaI extends CaI using Rényi divergence variational inference.
result Risk-sensitive optimal policy can be obtained by solving a soft Bellman equation.
Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this poli…
Paper establishes DRL for high-dimensional rewards.
problem Intractable reinforcement learning with high-dimensional rewards.
method Theoretical foundations and a novel DRL algorithm.
result Bellman operator contraction in high-dimensional spaces.
A contraction analysis improves model-based RL's error recovery.
problem Theoretical understanding of model-based reinforcement learning.
method Contraction analysis applied to both stochastic and deterministic state transitions.
result Error reduction in cumulative reward using branched rollouts.
Proposes RFQI for robust RL using offline data.
problem Learning robust policies in the presence of model uncertainty.
method RFQI algorithm using offline data to learn optimal robust policy.
result RFQI learns near-optimal robust policy under standard assumptions.
Recently, \citet{SuttonMW15} introduced the emphatic temporal differences (ETD) algorithm for off-policy evaluation in Markov decision processes. In this short note, we show that the projected fixed-point equation that underlies ETD involves a contraction operator, with a γ \sqrtγ γ -contraction modulus (where γ γ γ is the …
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option p…
New algorithm reduces switching costs in RL beyond linear MDPs.
problem Costly policy switching in reinforcement learning.
method ELEANOR-LowSwitching algorithm for linear Bellman-complete MDPs.
result Achieves near-optimal regret with logarithmic switching cost.