Thinking Forward and Backward: Effective Backward Planning with Large Language Models

TL;DR

This paper explores the advantages of backward planning with large language models, proposing a method that flips problems to improve planning success rates by leveraging asymmetries and reducing biases.

Contribution

The authors introduce a backward planning algorithm that flips problems and combines forward and backward planning, enhancing success rates in LLM-based planning tasks.

Findings

Backward planning performance correlates with problem complexity in that direction.

Flipping problems and planning forward in the flipped version improves success rates.

Combining bidirectional planning with self-verification increases success by 4-24%.

Abstract

Large language models (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.