Decision-Theoretic Planning: Structural Assumptions and Computational Leverage (1105.5460v1)

Abstract: Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives adopted in these areas often differ in substantial ways, many planning problems of interest to researchers in these fields can be modeled as Markov decision processes (MDPs) and analyzed using the techniques of decision theory. This paper presents an overview and synthesis of MDP-related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies or plans. Planning problems commonly possess structure in the reward and value functions used to describe performance criteria, in the functions used to describe state transitions and observations, and in the relationships among features used to describe states, actions, rewards, and observations. Specialized representations, and algorithms employing these representations, can achieve computational leverage by exploiting these various forms of structure. Certain AI techniques -- in particular those based on the use of structured, intensional representations -- can be viewed in this way. This paper surveys several types of representations for both classical and decision-theoretic planning problems, and planning algorithms that exploit these representations in a number of different ways to ease the computational burden of constructing policies or plans. It focuses primarily on abstraction, aggregation and decomposition techniques based on AI-style representations.

• The paper presents a unified decision-theoretic planning framework that exploits MDP structural properties to construct optimal or approximate policies.
• The authors detail specialized dynamic programming techniques, like value and policy iteration, to address both fully and partially observable planning challenges.
• The research offers actionable insights for designing scalable AI planning systems in robotics, control systems, and decision support applications.

Essay on "Decision Theoretic Planning: Structural Assumptions and Computational Leverage"

Authors:

Craig Boutilier, Thomas Dean, Steve Hanks

Abstract:

The paper "Decision Theoretic Planning: Structural Assumptions and Computational Leverage" explores the Markov Decision Processes (MDPs) as a unifying framework for decision-theoretic planning (DTP) problems under uncertainty. It provides an overview of MDP-related methods and highlights how structural properties of MDPs can be exploited for constructing optimal or approximately optimal policies. The authors discuss specialized representations and algorithms that leverage the structure in reward functions, transitions, and observations inherent in many planning problems, focusing on AI-style abstraction, aggregation, and decomposition techniques.

Overview:

Decision-theoretic planning addresses the challenge of making sequential decisions in uncertain environments by modeling these problems as Markov Decision Processes (MDPs). MDPs are characterized by a finite or countably infinite set of states, a set of actions available to the agent, transition probabilities between states conditional on actions, a reward function, and possibly a cost function. For planning under uncertainty, MDPs can represent and analyze various classes of problems using decision theory.

The paper synthesizes numerous techniques and methods related to MDPs and their application to AI planning. In doing so, the authors illustrate how structural properties of MDPs—such as certain regularities or patterns in state transitions, rewards, and observations—can be exploited to achieve computational efficiency. This can be particularly critical in large state spaces often encountered in AI planning problems.

Implications of the Research:

• Numerical Results and Strong Claims: The paper presents a detailed survey of the different methods and representations, primarily focusing on dynamic programming approaches like value iteration and policy iteration, and how they apply to fully observable MDPs (FOMDPs), partially observable MDPs (POMDPs), and specializations for deterministic and probabilistic planning frameworks. The computational complexity results indicate that while fully observable MDPs are P-complete, partially observable and more generalized planning problems pose a higher complexity, often being NP-hard or even undecidable.
• Theoretical Implications: The paper underscores the theoretical importance of structural properties in MDPs. By identifying and exploiting these properties, researchers can simplify and compress the representations of MDPs, making previously intractable problems more manageable. The use of abstraction, aggregation, and decomposition techniques from AI enriches the computational toolbox available for tackling decision-theoretic planning problems.
• Practical Applications: In practical terms, this research can significantly influence the design of planning algorithms in diverse fields like robotics, automated control systems, and decision support systems. The insights provided on leveraging structural properties could help in developing more efficient and scalable solutions, which is critical for real-world applications where computational resources are limited.

Speculations on Future Developments in AI:

• Enhanced Learning Algorithms: As the complexity of realistic planning problems continues to grow, future AI research might integrate more advanced learning algorithms with decision-theoretic planning frameworks. Techniques like reinforcement learning, especially in partially observable environments, could see further evolution by utilizing the structural MDP properties discussed in this paper.
• Real-time Decision Making: Another potential direction is the development of real-time decision-making algorithms that dynamically adapt as new information is received, further refining Real-time Dynamic Programming (RTDP) and online planning methods to deal efficiently with stochastic domains.
• Sophisticated Approximation Methods: Given the computational challenges highlighted for POMDPs and complex probabilistic planning scenarios, there is likely to be a surge in sophisticated approximation methods. Research could focus on scalable heuristics, sampling methods, and hybrid approaches that combine different strands of decision-theoretic and heuristic planning.

Conclusion:

The paper "Decision Theoretic Planning: Structural Assumptions and Computational Leverage" represents a comprehensive effort to consolidate various methods and approaches that utilize MDPs for planning under uncertainty. By focusing on structural properties and leveraging AI techniques, it provides a path toward efficiently solving complex planning problems. The theoretical insights and practical implications laid out in the paper pave the way for future advancements in AI, particularly in developing scalable, real-time decision-making algorithms.