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

TL;DR

A backward planning algorithm for LLMs is proposed that first flips the problem and then plans forward in the flipped problem, which helps avoid the backward bias, generate more diverse candidate plans, and exploit asymmetries between the forward and backward directions in planning problems.

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.

Figures (12)

• Figure 1: (Left) In planning problems such as navigation, it can often be easier to plan in the backward direction, especially when a "bottleneck" state (red node) exists and it is easier to find it from the goal rather than from the initial state. We consider Graph Planning, where the LLM needs to plan the shortest path from the initial node to the goal. (Right) Two other planning domains: Array Transformation, where an integer array is manipulated through different functions to the desired array, and Blocksworld, where stacks of blocks are re-oriented to the goal state.
• Figure 2: Sampling in forward or backward direction and then self-verifying the plans in Array Transformation.
• Figure 3: Success rates achieved by forward and backward planning in Graph Planning vs. difference between forward and backward BFS computations. The LLM plans better in the direction of fewer computations needed, but the forward direction outperforms backward in general.
• Figure 4: Flipping the problem and then plan in the new forward direction in Blocksworld (left) and Graph Planning with directed graph (Right).
• Figure 5: Fwd-Flip plans well even when the forward direction is difficult.