Heuristic-Guided Multi-Step Reasoning with Large Language Models: A POMDP Approach

Core Concepts

A novel planning-based approach, called Plan of Thoughts (PoT), that leverages a large language model's self-reflective reasoning capabilities to guide multi-step problem solving through a Partially Observable Markov Decision Process (POMDP) formulation.

Abstract

The paper presents a novel approach called Plan of Thoughts (PoT) that extends the previous Tree of Thoughts (ToT) method to enable more effective multi-step reasoning with large language models. The key contributions are: Formalizing the process of "thinking" and "reasoning" with a language model as a POMDP, where the language model's own reflections about the value of a state are used as a search heuristic. Leveraging the online POMCP solver, PoT demonstrates superior success rate of 89.4% on the Game of 24 task compared to existing approaches, while also offering better anytime performance characteristics. The PoT approach works as follows: The problem is represented as a POMDP with states S = S × U, where s ∈ S are the sub-steps of the decomposed problem and u ∈ U represent the unobservable, true underlying value being estimated. The actions A = {continue, rollback, think} allow the agent to expand the current branch, backtrack, or generate a new thought. The observations O ∈ S × U are the language model's judgments about the value of a given state, obtained by asking the model to rate the state as "sure", "likely", or "impossible". The transition function T and reward function R are defined based on the problem structure and language model evaluations. By solving this POMDP using the anytime POMCP solver, PoT is able to dynamically explore the most promising paths while maintaining strong anytime performance, outperforming previous approaches like ToT and Chain-of-Thought on the Game of 24 task. The authors also demonstrate a hybrid language modeling approach, using GPT-3.5-Turbo-Instruct for thought generation and GPT-4-Turbo for evaluation, which allows for more efficient problem solving.

Stats

The Game of 24 task involves combining four numbers using basic arithmetic operations to reach a target value of 24. The dataset used is the same as the one curated by Yao et al. for the ToT approach, scraped from 4nums.com and sorted by difficulty.

Quotes

"By combining explicit planning and LM reasoning, this approach achieved state-of-the-art results on the Game of 24 and other difficult natural-language tasks such as a crossword." "Importantly, the anytime property of the approach presented here indicates that PoT can scale its solution time dynamically to the number of 'thoughts' required for each problem as shown by the AUC value of 81.4% of our approach using time as a threshold, while ToT will take a fix-time approach to generate and evaluate an entire tree regardless of solution complexity."

Key Insights Distilled From

Plan of Thoughts: Heuristic-Guided Problem Solving with Large Language Models

by Houjun Liu at arxiv.org 05-01-2024

https://arxiv.org/pdf/2404.19055.pdf

Deeper Inquiries

How can the PoT approach be extended to handle more complex, open-ended reasoning tasks beyond the Game of 24

To extend the Plan of Thoughts (PoT) approach to handle more complex, open-ended reasoning tasks beyond the Game of 24, several key strategies can be implemented: Enhanced Problem Decomposition: Develop more sophisticated methods for decomposing complex problems into manageable sub-tasks. This could involve hierarchical decomposition, where higher-level goals are broken down into smaller, more achievable objectives. Dynamic State Evaluation: Implement a mechanism for dynamic evaluation of the state value heuristics provided by the language model. This could involve incorporating feedback loops that adjust the weighting of heuristic signals based on the progress made in solving the problem. Adaptive Action Selection: Introduce adaptive action selection strategies that allow the system to choose between different types of actions based on the current state of the problem. This could involve incorporating reinforcement learning techniques to learn optimal action policies. Integration of External Knowledge: Incorporate external knowledge sources or domain-specific information to enhance the reasoning capabilities of the language model. This could involve pre-training the model on relevant datasets or integrating external databases for additional context. Transfer Learning: Explore the use of transfer learning techniques to leverage knowledge gained from solving one type of problem to improve performance on a different, but related, task. This could involve fine-tuning the language model on a diverse set of tasks to improve its generalization capabilities. By incorporating these strategies, the PoT approach can be extended to tackle a broader range of complex, open-ended reasoning tasks with improved efficiency and effectiveness.

What are the potential limitations of using language model-based heuristics as the sole guiding mechanism for multi-step problem solving, and how could these be addressed

Using language model-based heuristics as the sole guiding mechanism for multi-step problem solving may present several potential limitations: Limited Generalization: Language models may struggle to generalize to unseen or complex scenarios, leading to suboptimal performance on novel tasks that require creative problem-solving approaches. Bias and Error Propagation: Language models are susceptible to biases present in the training data, which can lead to erroneous or misleading heuristic signals. These biases can propagate throughout the reasoning process, impacting the quality of the solutions generated. Computational Overhead: The computational cost of repeatedly querying the language model for heuristic evaluations can be significant, especially for large-scale problems or real-time applications, leading to scalability challenges. To address these limitations, a few strategies can be considered: Ensemble Approaches: Combine multiple language models with diverse training data to mitigate biases and errors, improving the robustness of the heuristic signals. Human-in-the-Loop Validation: Integrate human feedback loops to validate and correct the reasoning process, ensuring that the solutions generated are accurate and aligned with human expectations. Hybrid Models: Explore hybrid models that combine symbolic reasoning techniques with language model-based heuristics to leverage the strengths of both approaches and mitigate their respective weaknesses. By incorporating these strategies, the limitations of using language model-based heuristics for multi-step problem solving can be mitigated, enhancing the overall performance and reliability of the approach.

Given the computational expense of the PoT approach, how could the efficiency of the method be further improved to make it more practical for real-world applications

To improve the efficiency of the PoT approach and make it more practical for real-world applications, several optimization techniques can be implemented: Model Pruning: Implement model pruning techniques to reduce the size and complexity of the language model used for heuristic evaluations. This can help streamline the inference process and reduce computational overhead. Caching Mechanisms: Introduce caching mechanisms to store and reuse previously computed heuristic evaluations, reducing redundant computations and speeding up the reasoning process. Parallelization: Utilize parallel computing techniques to distribute the workload across multiple processors or GPUs, enabling faster processing of multiple sub-tasks simultaneously. Hardware Acceleration: Leverage hardware accelerators such as GPUs or TPUs to expedite the inference process and improve the overall performance of the PoT approach. Optimized Sampling Strategies: Develop optimized sampling strategies to efficiently explore the solution space and prioritize promising paths, reducing the number of iterations required for problem solving. By implementing these efficiency-enhancing techniques, the PoT approach can be optimized for real-world applications, enabling faster and more scalable multi-step problem solving with language models.