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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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316394125 · Jun 202019922001200920172026
48 results for probabilistic Bellman backup

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.

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.

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.

Off-policy reinforcement learning aims to leverage experience collected from prior policies for sample-efficient learning. However, in practice, commonly used off-policy approximate dynamic programming methods based on Q-learning and actor-critic methods are highly sensitive to the data distribution, and can make only …

2019-06-03abs ↗pdf ↗

A new algorithm reduces training time for distributed machine learning by dynamically assigning backup workers.

problem Time-consuming synchronization phase due to slow workers (stragglers).
method Dynamic allocation of backup workers to minimize waiting time.
result Achieves linear speedup in convergence performance with more workers.

Value-based reinforcement learning (RL) methods like Q-learning have shown success in a variety of domains. One challenge in applying Q-learning to continuous-action RL problems, however, is the continuous action maximization (max-Q) required for optimal Bellman backup. In this work, we develop CAQL, a (class of) algor…

2019-09-26abs ↗pdf ↗

SUNRISE improves off-policy RL algorithms by integrating ensemble methods.

problem Stability and exploration issues in off-policy RL algorithms.
method SUNRISE combines ensemble-based weighted Bellman backups and upper-confidence bounds for efficient exploration.
result SUNRISE improves the performance of off-policy RL algorithms across various domains.

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the …

2011-05-04abs ↗pdf ↗

FOCAL tackles offline meta-reinforcement learning with efficient task inference and behavior regularization.

problem Efficiently adapt RL algorithms to unseen tasks without interactions, addressing bootstrapping errors and robust task inference.
method FOCAL combines behavior regularization, a deterministic context encoder, and a negative-power distance metric for efficient task inference.
result FOCAL outperforms prior algorithms on meta-RL benchmarks, demonstrating computational efficiency.

The paper proves well-posedness of nonlocal PDEs related to stochastic control problems.

problem Characterizing equilibrium strategies and value functions for time-inconsistent stochastic control problems.
method Method of continuity and Banach's fixed point arguments, with Schauder prior estimates.
result Global well-posedness of nonlocal fully nonlinear PDEs with sharp a-priori estimates.

Optimal control theory connects diffusion models to generative modeling.

problem Sampling from unnormalized densities in statistics and computational sciences.
method Deriving a Hamilton-Jacobi-Bellman equation and applying control theory to minimize Kullback-Leibler divergence.
result Time-reversed diffusion sampler (DIS) outperforms other diffusion-based sampling methods.

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.

Reinforcement learning has attracted great attention recently, especially policy gradient algorithms, which have been demonstrated on challenging decision making and control tasks. In this paper, we propose an active multi-step TD algorithm with adaptive stepsizes to learn actor and critic. Specifically, our model cons…

2019-11-11abs ↗pdf ↗

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.

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.

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.

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…

2014-07-09abs ↗pdf ↗

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.

In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the und…

2019-12-05abs ↗pdf ↗

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)\mathcal{O}(d) in the action space finite case, and automatically adapts to bias-variance tradeoff.

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.

Paper analyzes convergence of Sinkhorn algorithm for discrete probability measures on torus.

problem Achieving exponential convergence of Sinkhorn algorithm in general settings.
method Coupling by reflection techniques for controlled diffusions on the torus.
result Proves pointwise exponential convergence of Sinkhorn iterates and their gradient.

In the landscape of TD algorithms, the Q(σσ, λλ) algorithm is an algorithm with the ability to perform a multistep backup in an online manner while also successfully unifying the concepts of sampling with using the expectation across all actions for a state. σ[0,1]σ\in [0, 1] indicates the extent to which sampling is use…

2019-12-21abs ↗pdf ↗

Decouples critic chunk length from policy to improve policy reactivity and performance.

problem Bootstrapping bias and difficulty in extracting optimal policies from chunked critics.
method Optimizes policy against a distilled critic for partial action chunks, allowing shorter chunks for policy.
result Reliably outperforms prior methods on long-horizon offline goal-conditioned tasks.

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 …

2016-10-29abs ↗pdf ↗

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.