arxiv_ml 90% Match Research Paper RL Researchers,AI Theorists,Robotics Engineers,Algorithm Designers 2 weeks ago

On the hardness of RL with Lookahead

reinforcement-learning › robotics-rl

📄 Abstract

Abstract: We study reinforcement learning (RL) with transition look-ahead, where the agent may observe which states would be visited upon playing any sequence of $\ell$ actions before deciding its course of action. While such predictive information can drastically improve the achievable performance, we show that using this information optimally comes at a potentially prohibitive computational cost. Specifically, we prove that optimal planning with one-step look-ahead ($\ell=1$) can be solved in polynomial time through a novel linear programming formulation. In contrast, for $\ell \geq 2$, the problem becomes NP-hard. Our results delineate a precise boundary between tractable and intractable cases for the problem of planning with transition look-ahead in reinforcement learning.

Authors (5)

Corentin Pla

Hugo Richard

Marc Abeille

Nadav Merlis

Vianney Perchet

Submitted

October 22, 2025

arXiv Category

stat.ML

arXiv PDF

Key Contributions

Establishes a precise boundary for the computational hardness of reinforcement learning with transition lookahead. It proves that one-step lookahead is polynomial-time solvable via linear programming, while two or more steps become NP-hard, highlighting the significant computational cost of advanced predictive information.

Business Value

Provides crucial theoretical insights for designing practical RL systems, guiding developers on the feasibility of incorporating lookahead mechanisms based on computational constraints.

Paper Metadata

Innovation Type

Theoretical

Deployment Feasibility

Low for deep lookahead (>=2 steps) due to NP-hardness, but high for single-step lookahead.

Limitations Addressed

Prohibitive computational cost of optimal lookahead planning,Lack of clear understanding of complexity boundaries in RL lookahead

Performance Gains

Not applicable, focuses on theoretical complexity.

Technical Tags

Reinforcement LearningLookahead PlanningComputational ComplexityNP-HardnessLinear ProgrammingState SpaceAction SequencesDecision MakingOptimal PlanningTractability Boundary

Research Topics

Theoretical RLAlgorithmic ComplexityPlanning Under UncertaintyComputational Theory

Methods & Architectures

Linear Programming FormulationComplexity Analysis (NP-hardness proof)

Applications & Tasks

Robotics Game Playing Operations Research Autonomous Systems Computational hardness of planningOptimizing lookahead in RLDelineating tractable vs. intractable RL problems Optimal Policy PlanningDecision Making with Future State Prediction

Related Fields

Computer Science TheoryOperations ResearchArtificial IntelligenceControl Theory

Keywords

Reinforcement LearningLookaheadPlanningComputational ComplexityNP-hardLinear ProgrammingState PredictionDecision TheoryTractabilityRL AlgorithmsAutonomous SystemsRoboticsGame Theory

Academic Context

#Theoretical RL#Algorithmic Complexity#Planning Under Uncertainty#Computational Theory

Commercial Potential

Target Industries

RoboticsGamingAutonomous VehiclesLogistics

Use Case Examples

Robots planning complex manipulation tasksGame AI with predictive capabilitiesOptimizing resource allocation in dynamic environments

Competitive Edge

Establishes a fundamental theoretical limit on the use of lookahead in RL, informing the design space for future algorithms.

Resource Requirements

Compute Needs

Polynomial for 1-step lookahead, potentially exponential for >=2 steps.

Data Requirements

Not applicable, theoretical analysis.

Deployment Constraints

Significant computational resources required for lookahead planning, especially for complex environments or longer lookahead horizons.

Scalability

Scalability is limited by computational complexity, particularly for multi-step lookahead.

Production Readiness

Maturity Level

Theoretical Foundation

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