What type of inference is planning? (2406.17863v4)

Abstract: Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about "planning as inference"? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

• The paper introduces a unified variational inference framework that reweights entropy terms to compare marginal, MAP, and MMAP inference for planning.
• The paper formulates a novel planning inference type and demonstrates its optimality in deterministic settings and robustness in stochastic MDPs using value belief propagation.
• Empirical validations on synthetic MDPs and International Planning Competition tasks confirm that the proposed approach outperforms traditional inference methods under high stochasticity.

What Type of Inference is Planning?

The paper "What type of inference is planning?" by Miguel Lázaro-Gredilla, Li Yang Ku, Kevin P. Murphy, and Dileep George addresses a significant question in the domain of probabilistic graphical models and decision-making processes. The authors explore the various types of inference associated with probabilistic graphical models, such as marginal, maximum-a-posteriori (MAP), and marginal MAP (MMAP), and their applicability and relevance to the task of planning.

Core Contributions

The paper makes several noteworthy contributions. Primarily, it introduces a unified variational inference (VI) framework to analyze and compare different types of inference in the context of planning. This framework enables a categorization and ranking of various inference techniques based on their utility in planning tasks. The primary findings and innovations of the paper can be summarized as follows:

1. Unified Variational Framework: The authors show that different types of inference, such as marginal, MAP, and MMAP, can be viewed as different weightings of the entropy term in a variational problem. This insight facilitates a consistent comparison across these techniques.
2. Novel Planning Inference Type: Planning is identified as a distinct type of inference that is not exactly represented by any commonly used methods under stochastic dynamics. The paper provides a precise formulation of this planning inference type, describing it as a unique set of weightings in the variational framework.
3. Approximate Planning in Factored-State MDPs: By leveraging an analogue of loopy belief propagation (LBP), the authors propose methods to perform approximate planning in factored-state Markov decision processes (MDPs) efficiently. This addresses the intractability problem associated with large state spaces in such MDPs.
4. Characterization of Inference Types: The authors empirically validate their theoretical results using synthetic MDPs and tasks from the International Planning Competition, providing insights into the performance and suitability of different inference types under varying conditions of stochasticity.

Detailed Analysis

Variational Inference Framework

The variational framework introduced in the paper allows direct comparisons between different types of inference. By framing these types as variational problems with different entropy terms, the authors can systematically account for their performance in planning tasks. Specifically, the distinctions among marginal inference, MAP inference, and MMAP are delineated by their respective entropy terms within the VI framework.

Computational Techniques

A major innovation is the introduction of value belief propagation (VBP), an extension of LBP tailored for planning. This technique allows for the approximation of planning solutions in factored-state MDPs without succumbing to the exponential growth of the state space. The paper's demonstration of VBP’s practical applicability underscores its value for solving real-world planning problems.

Furthermore, the authors provide proofs and derivations to support the theoretical basis of their approach, ensuring the robustness of their results. For example, they show that the planning inference type yields optimal policies in environments with deterministic dynamics and that it remains theoretically superior when dealing with stochastic dynamics.

Empirical Validation

The paper's empirical validations include tests on synthetic MDPs and benchmarks from the International Planning Competition. These experiments highlight the superiority of the proposed planning inference type under moderate to high stochastic dynamics. It also exposes the inadequacy of established methods like MMAP and MAP in such scenarios due to their inherent lack of reactivity and integration over trajectories.

Implications and Future Work

The insights provided by this paper have substantial implications for both theoretical research and practical applications. The variational framework can serve as a foundation for developing new inference algorithms tailored for specific planning scenarios. The understanding of the relative merits and limitations of different inference types can guide practitioners in choosing appropriate methods for their specific applications, particularly in fields like robotics and automated decision-making.

The paper also opens avenues for future research to explore deeper integrations of VI techniques with other planning methods, particularly in settings with non-stationary dynamics or complex reward structures. The introduction of VBP as a tractable solution for factored MDPs invites further exploration into its potential optimizations and extensions.

In sum, the paper by Lázaro-Gredilla et al. offers a rigorous and insightful analysis of the intersection between inference and planning. It not only clarifies the conceptual underpinnings of different inference techniques but also provides practical tools and methodologies for improving planning algorithms in complex, stochastic environments.