Paper analyzes distributional reinforcement learning with value function approximation, introducing Bellman unbiasedness and a new algorithm.
problem Improving reinforcement learning by capturing environmental stochasticity and addressing infinite dimensionality.
method Introduces Bellman unbiasedness and proposes SF-LSVI algorithm for provably efficient distributional reinforcement learning.
result Achieves a tight regret bound of O(d_E H^3/2 √K) for distributional reinforcement learning.
Modified relative universality for unbiasedness and consistency in dimension reduction.
problem Gap in proof of unbiasedness and Fisher consistency in relative universality.
method Modified definition of relative universality using ǫ-measurability.
result Established unbiasedness and Fisher consistency rigorously.
Random Forest permutation importance measure is asymptotically unbiased in sparse regression models.
problem Challenges in selecting informative variables in high-dimensional regression problems.
method Theoretical guarantees and asymptotic unbiasedness of permutation importance measure under specific assumptions.
result Permutation importance measure in Random Forest is asymptotically unbiased.
We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset…
The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures of risk measures in terms of bias. We show that once the parameters of a model ne…
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.
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.
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.
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.
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.
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.
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.
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…
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…
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…
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.
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. We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the embedded manifolds also converge to deterministic limits. Particularly interestin…
Optimal reconciliation keeps some forecasts unchanged in hierarchical forecasting.
problem Keeping some forecasts unchanged in hierarchical forecasting.
method Formulates a method to keep some forecasts unchanged in a hierarchical forecasting system.
result Preserves unbiasedness and non-negativity of forecasts.
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.
This work improves texture segmentation by automatically tuning hyperparameters for Total-Variation.
problem The challenge is to automatically select hyperparameters for Total-Variation texture segmentation.
method The approach involves extending Stein's unbiased gradient estimator to handle correlated Gaussian noise, leading to an automatic tuning method.
result The method provides an automatic way to select hyperparameters for Total-Variation texture segmentation.
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.
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.
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.
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.
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.
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.
In this letter we investigate the information provided by the "compass rose" (Crack, T.F. and Ledoit, O. (1996), Journal of Finance, 51(2), pg. 751-762) patterns revealed in phase portraits of daily stock returns. It has been initially suggested that the compass rose is just a manifestation of price clustering and disc…
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.
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…
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.
Deep learning for HJB PDEs using synthetic data and residual minimization.
problem Solving Hamilton-Jacobi-Bellman PDEs for optimal control problems.
method Gradient-augmented synthetic dataset for supervised learning, residual minimization.
result Improves accuracy and efficiency of deep learning for HJB PDEs.
New method solves continuous time mean-variance model for consistent investment strategy.
problem Time-consistent optimal strategy for continuous time mean-variance model.
method Developed a new Bellman principle method.
result Obtained a time-consistent dynamic optimal strategy.
A new estimator combines bootstrapping and rollout methods in RL.
problem Combining strengths of bootstrapping and rollout methods in RL.
method Subgraph Bellman operators and fixed point solving.
result Upper bound on error approaches optimal TD variance with additional term.
Paper solves investment strategy optimization with deep learning.
problem Maximizing investor utility with optimal asset allocation.
method Solves PDEs with Deep Galerkin method.
result Deep learning algorithm outperforms finite difference method.
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.
New algorithms reduce complexity for learning in MDPs with entropy regularization.
problem Efficient learning for MDPs with large or continuous state and action spaces.
method Multilevel Monte Carlo (MLMC) algorithms integrating fixed-point iteration and stochastic approximation of the Bellman operator.
result MLMC with unbiased approximation of the Bellman operator achieves polynomial sample complexity.
New BE dimension measure reveals rich RL problems with sample-efficient algorithms.
problem Finding sample-efficient algorithms for complex RL problems.
method Introducing Bellman Eluder (BE) dimension and designing GOLF and OLIVE algorithms.
result GOLF and OLIVE algorithms learn near-optimal policies for low BE dimension problems with polynomial samples.