Reasoning About Beliefs and Actions Under Computational Resource Constraints (1304.2759v1)

Abstract: Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete normative analysis impossible. We attempt to move discussion beyond the debate over the scope of problems that can be handled effectively to cases where it is clear that there are insufficient computational resources to perform an analysis deemed as complete. Under these conditions, we stress the importance of considering the expected costs and benefits of applying alternative approximation procedures and heuristics for computation and knowledge acquisition. We discuss how knowledge about the structure of user utility can be used to control value tradeoffs for tailoring inference to alternative contexts. We address the notion of real-time rationality, focusing on the application of knowledge about the expected timewise-refinement abilities of reasoning strategies to balance the benefits of additional computation with the costs of acting with a partial result. We discuss the benefits of applying decision theory to control the solution of difficult problems given limitations and uncertainty in reasoning resources.

• The paper introduces approximation and heuristic strategies to manage complex belief updating and decision making under strict resource limits.
• It demonstrates a timewise-refinement paradigm that incrementally improves inference quality as more computational resources become available.
• The study advocates for bounded rationality, promoting alternative strategies to classical methods for enhancing practical AI systems.

Reasoning About Beliefs and Actions Under Computational Resource Constraints

Eric J. Horvitz's paper, "Reasoning About Beliefs and Actions Under Computational Resource Constraints," addresses the significant challenges encountered when implementing decision-making frameworks consistent with probability and utility theory under stringent computational and engineering constraints. This work explores the complexities inherent in the application of formal decision-theoretic frameworks to real-world, high-stakes environments, such as medical decision-support systems, where resource limitations hinder the ability to perform complete normative analysis.

Core Concepts

The paper breaks down the problem into several key components:

1. Problem Formulation, Belief Entailment, and Decision Making: These are identified as the primary tasks in uncertain reasoning. Problem formulation concerns the modeling of the reasoning problem, belief entailment involves updating beliefs in response to new evidence, and decision making is about choosing the best action based on updated beliefs.
2. Normative Basis vs. Real-World Application: While probability and utility theories provide a solid framework for reasoning under uncertainty, their practical application is limited by their inherent computational demands. Real-world problems in AI, especially those involving complex decisions under uncertainty, often surpass the capabilities offered by classical frameworks without sufficient computational resources.
3. Bounded Rationality and Inference Under Constraints: The paper underscores the importance of bounded rationality, suggesting that in environments where resource constraints prevent complete normative reasoning, alternative strategies—such as approximations and heuristics—can present higher expected utility despite being suboptimal.

Techniques and Strategies

Horvitz explores various methods to allow intelligent systems to function effectively under resource constraints:

• Approximation Techniques: These include strategies like bound calculation and stochastic simulation, which provide controllable trade-offs between accuracy and computational expense.
• Heuristic Strategies: These involve methods such as completeness modulation, abstraction modulation, and heuristic imposition of independence assumptions. Such approaches aim to manage complexity and enable tractable solutions by focusing attention on the most relevant parts of the problem.
• Timewise-Refinement Paradigm: This paradigm advocates for the development of inference systems that can produce partial solutions incrementally, improving their quality as more computational resources become available.

Implications and Future Directions

The implications of Horvitz's work are profound for the development of AI systems that need to make decisions under uncertainty with limited time and resources. It emphasizes the need for future AI research to incorporate flexible, resource-aware strategies in designing decision-support systems. By considering the comprehensive value of computational processes—accounting for both object-related and inference-related values—AI systems can optimize their utility in practical situations.

The paper suggests that the integration of knowledge about computational costs and the expected refinement of results over time is essential for improving the utility of AI systems in dynamic environments. The framework proposed by Horvitz forms the basis for further research into developing intelligent control strategies that can adaptively select among various reasoning strategies based on the context and resource availability.

In conclusion, Horvitz's exploration of reasoning under constraints extends the applicability of AI in real-world settings by offering a structured approach to managing resources effectively while maximizing decision utility. This work paves the way for more robust, adaptable systems capable of functioning in resource-limited environments, an essential step towards building truly intelligent, autonomous agents.