Thinking Forward and Backward: Effective Backward Planning with Large Language Models (2411.01790v1)

Abstract: LLMs have exhibited remarkable reasoning and planning capabilities. Most prior work in this area has used LLMs to reason through steps from an initial to a goal state or criterion, thereby effectively reasoning in a forward direction. Nonetheless, many planning problems exhibit an inherent asymmetry such that planning backward from the goal is significantly easier -- for example, if there are bottlenecks close to the goal. We take inspiration from this observation and demonstrate that this bias holds for LLM planning as well: planning performance in one direction correlates with the planning complexity of the problem in that direction. However, our experiments also reveal systematic biases which lead to poor planning in the backward direction. With this knowledge, we propose a backward planning algorithm for LLMs that first flips the problem and then plans forward in the flipped problem. This helps avoid the backward bias, generate more diverse candidate plans, and exploit asymmetries between the forward and backward directions in planning problems -- we find that combining planning in both directions with self-verification improves the overall planning success rates by 4-24% in three planning domains.

• The paper demonstrates that LLMs are inherently biased toward forward planning, which creates bottlenecks near the goal.
• It introduces a novel strategy by flipping problem states, leading to a 4-24% improvement in planning success rates across multiple domains.
• The method leverages self-verification and BFS analysis to provide actionable insights for enhancing AI planning in robotics and data manipulation.

LLMs in Bidirectional Planning: Addressing Backward Planning Bias

The paper under analysis focuses on leveraging LLMs for solving planning tasks. In the context of planning, existing research predominantly emphasizes forward planning, wherein an LLM maps a sequence of steps from a defined initial state to a specified goal. However, the authors highlight a crucial asymmetry within many planning problems—specifically bottlenecks located near the goal—that can impede this forward-centric approach. This document explores the utility of backward planning in circumventing these bottlenecks and presents a novel method to improve LLM performance by flipping planning problems.

Core Contributions and Findings

The paper initiates its empirical journey through three classical planning domains—Graph Planning, Array Transformation, and Blocksworld—demonstrating that LLMs are inherently biased towards forward planning. The authors attribute this bias to the autoregressive nature of LLMs, which favor sequence generation beginning from an origin state.

To address this, the paper introduces a backward planning strategy that resembles human deductive reasoning tactics by generating steps from the goal backward to the start. However, their results initially illustrate a systematic underperformance in backward planning when compared to forward planning. Guided by these findings, the authors propose a solution involving the transformation of planning problems such that the goal state becomes the initial state and vice versa—an operation termed "flipping."

This strategy effectively capitalizes on the LLM’s structural biases by converting backward planning problems into forward ones. Experiments show a notable improvement of 4-24% in planning success rates across the examined domains when LLMs generated plans from both the original and flipped problem states.

Experimental Insights

The researchers executed extensive experiments across the aforementioned domains to test their hypotheses. Their systematic approach involved analyzing computational steps needed in both forward and backward directions using Breadth-First Search (BFS). The key results revealed that LLMs naturally perform better in the direction requiring fewer BFS computations, although inherently biased towards forward planning.

An interesting methodological addition is the practice of self-verification, allowing LLMs to critically evaluate generated plans to ensure their validity. This not only assures optimal path identification but also aids in circumventing LLM's biases through iterative candidate selection.

Theoretical and Practical Implications

Theoretically, this work challenges the directional bias of LLMs in planning tasks, proposing a more human-like, flexible approach. It shows that reversing the planning process can exploit inherent problem asymmetries to the LLM's advantage, effectively broadening the range of solvable tasks. Practically, the insights can be applied in real-world applications such as robotics navigational tasks, complex data manipulations like array transformations, and cognitive simulations for human-like reasoning in machines.

Speculations on Future Developments

Future research can focus on fine-tuning LLMs to enhance backward reasoning capabilities intrinsically, possibly leveraging reinforcement learning or additional training datasets focused on backward problem-solving. The methodical integration of LLMs with classical planning approaches can also yield hybrid systems improving both efficiency and adaptability.

Moreover, exploring LLMs' ability to self-assess problem structures and automatically decide optimal bidirectional pathways holds promise. This adaptive reasoning could forge new frontiers in autonomous systems where machines mimic human decision-making processes.

In conclusion, this paper articulates a compelling argument for integrating backward thinking in LLM-based planning, providing a scalable methodology with the potential to advance artificial intelligence capabilities in complex planning scenarios. The document sets a constructive precedent for future work in the bidirectional planning paradigm.