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.
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.
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.
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.
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.
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.
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 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.
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 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.
Study shows offline RL under Q⋆-approximation and partial coverage is harder than previously thought.
problem Theoretical limits of offline reinforcement learning under Q⋆-approximation and partial coverage. method Introduced a decision-estimation framework to decompose offline RL complexity into decision and value estimation errors.
result Answered the open question by proving sample inefficiency under partial coverage is not guaranteed by Q⋆-realizability and Bellman completeness. Paper introduces v-CMC linking causality and utility.
problem Linking causality and utility for value theory.
method Developed a new causal independence principle (v-CMC) and proved its equivalence.
result Equivalence of local, global, and decomposition versions of v-CMC.
The Bellman error is a poor proxy for value function accuracy, even with all state-action pairs.
problem The Bellman error is a poor proxy for the accuracy of the value function.
method Study of the Bellman equation as a surrogate objective for value prediction accuracy.
result The magnitude of the Bellman error is only weakly related to the distance to the true value function, even with all state-action pairs.
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact…
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.
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.
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.
New method uses TT approximations to solve HJB equations for efficient sampling.
problem Efficiently sampling from complex probability densities.
method Direct time integration of HJB equations using Tensor Train compression.
result Sample-free, dimensionality-avoiding integration method.
Develops deep learning methods for solving S-shaped utility maximisation problems.
problem Optimizing portfolios with S-shaped utility and random benchmarks.
method Uses deep learning and duality methods to solve the Hamilton-Jacobi-Bellman equation and adjoint equation.
result Demonstrates the accuracy of deep learning methods for non-concave utility maximisation problems.
We obtain the classical Hanner inequalities by the Bellman function method. These inequalities give sharp estimates for the moduli of convexity of Lebesgue spaces. Easy ideas from differential geometry help us to find the Bellman function using neither "magic guesses" nor calculations.
Richard Bellman's Principle of Optimality, formulated in 1957, is the heart of dynamic programming, the mathematical discipline which studies the optimal solution of multi-period decision problems. In this paper, we look at the main trading principles of Jesse Livermore, the legendary stock operator whose method was pu…
Solves infinite horizon portfolio problem with path-dependent labor income.
problem Infinite horizon portfolio choice with path-dependent labor income.
method Solves an infinite dimensional stochastic optimal control problem using explicit solutions to the HJB equation.
result Explicit solutions to the optimal controls in feedback form are found.
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 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.
The paper analyzes optimal consumption with past spending maximum as a reference.
problem Optimal consumption with past spending maximum as a reference.
method Path-dependent exponential utility, Hamilton-Jacobi-Bellman (HJB) equation, dual transform, smooth-fit principle.
result Closed-form solutions for optimal investment and consumption strategies in each region.
We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in term…
One-step Bellman alignment improves online RL by reducing task mismatch.
problem Online RL struggles with task similarity defined by rewards or transitions.
method One-step Bellman alignment and re-weighted targeting (RWT) to correct task mismatch.
result Regret bounds show task shift complexity, not target MDP, affects performance.
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) in the action space finite case, and automatically adapts to bias-variance tradeoff. A new reinforcement learning method for robots thinking and moving simultaneously.
problem Concurrent control in robotic systems where actions must be decided while the system is still evolving.
method Continuous-time Bellman equations, discretization aware of system delays, and architectural extension to deep reinforcement learning.
result The method successfully handles tasks requiring simultaneous decision-making and action execution.
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.
Paper introduces dynamic strategies for multi-period investment models.
problem Optimizing investment strategies over multiple periods with risk and return considerations.
method Developed a Bellman principle for discrete time multi-period mean-variance models, leading to dynamic optimal strategies and efficient frontiers.
result Dynamic optimal strategies can achieve higher returns with lower risk compared to the 1/n strategy.
Model quantifies uncertainty's impact on European option prices.
problem Uncertainty in market volatility risk affects option pricing.
method Hamilton-Jacobi-Bellman framework and finite element method.
result Dependence of Delta on uncertainty is nonlinear and varied.
This paper studies systematic exploration for reinforcement learning with rich observations and function approximation. We introduce a new model called contextual decision processes, that unifies and generalizes most prior settings. Our first contribution is a complexity measure, the Bellman rank, that we show enables …
Study solves optimal portfolio selection using HJB equation.
problem Optimal portfolio selection problem.
method Maximal monotone operator method, Banach fixed-point theorem, Fourier transform, monotone operators technique.
result Existence and uniqueness of solution to HJB equation.
Deep Bellman Hedging uses reinforcement learning to optimize financial portfolio hedging.
problem Optimizing financial portfolio hedging with derivatives and trading frictions.
method Actor-critic reinforcement learning algorithm with continuous state and action spaces.
result Trained model provides optimal hedge for any initial portfolio and market state.
We apply stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to minimize her probability of lifetime ruin. Without relying on the dynamic programming…
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.
Unified coverage analysis for linear off-policy evaluation in reinforcement learning.
problem Lack of a unified understanding of coverage parameters in linear off-policy evaluation.
method Developed a novel finite-sample analysis for LSTDQ algorithm, introducing feature-dynamics coverage.
result Unified understanding of coverage parameters in linear off-policy evaluation.
Lorentz-Finsler geometry reveals new and old inequalities.
problem Finding new inequalities using Lorentz-Finsler geometry.
method Applying reverse Cauchy-Schwarz and reverse triangle inequalities in Lorentz-Finsler geometry.
result Proved new and refined inequalities, including refinements of Aczél's inequality.
The paper analyzes risk bounds and Rademacher complexity in batch RL.
problem Estimating/minimizing Bellman error with general value function approximation.
method Characterizes generalization performance using Rademacher complexities of function classes.
result Risk bounds and Rademacher complexities provide insights into batch RL.
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.
Study optimal investment and consumption in a stochastic factor model.
problem Optimal investment and consumption decisions in a stochastic factor model.
method Characterization of well-posedness, numerical algorithm, and general theory of sub- and supersolutions for HJB equation.
result Proves existence and provides bounds for the solution to the HJB equation.
Deep neural nets approximate high-dimensional HJB equations efficiently.
problem Approximating solutions to high-dimensional HJB equations.
method Deep neural networks for approximating solutions.
result Deep neural networks can approximate solutions without the curse of dimensionality.
Optimal portfolio tracking with dynamic capital injection into a ratcheting benchmark.
problem Optimizing a portfolio's performance by dynamically adding capital to a non-decreasing benchmark.
method Formulated as an unconstrained control problem with a running maximum cost, transformed into an auxiliary problem with a nonlinear HJB equation, solved using probabilistic representation and stochastic flow analysis.
result Established the existence of a unique classical solution to the HJB equation, providing feedback optimal portfolio strategies.
Optimizes portfolios with costs, showing existence of optimal strategies.
problem Risk-sensitive portfolio optimization with transaction costs.
method Log-return i.i.d. framework, Bellman equation analysis.
result Existence of optimal strategies for risk-averse and risk-seeking cases.
In this paper, we consider the stochastic iterative counterpart of the value iteration scheme wherein only noisy and possibly biased approximations of the Bellman operator are available. We call this counterpart as the approximate value iteration (AVI) scheme. Neural networks are often used as function approximators, i…
New RL algorithm minimizes distributional learning error.
problem Improving distributional reinforcement learning for better error minimization.
method Proposes a new model-based algorithm with theoretical minimax optimality.
result Proves minimax optimality for approximating return distributions.
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.