The Trembling-Hand Problem for LTLf Planning

TL;DR

This paper addresses the challenge of planning under action instruction errors in temporal goal achievement, proposing methods to synthesize strategies that maximize success probability despite trembling hand faults.

Contribution

It introduces novel solution techniques using Markov Decision Processes for planning under trembling hand errors in LTLf goals, covering both deterministic and nondeterministic domains.

Findings

Proposed methods are formally correct.

Techniques effectively handle both deterministic and nondeterministic cases.

Experimental results demonstrate practical feasibility.

Abstract

Consider an agent acting to achieve its temporal goal, but with a "trembling hand". In this case, the agent may mistakenly instruct, with a certain (typically small) probability, actions that are not intended due to faults or imprecision in its action selection mechanism, thereby leading to possible goal failure. We study the trembling-hand problem in the context of reasoning about actions and planning for temporally extended goals expressed in Linear Temporal Logic on finite traces (LTLf), where we want to synthesize a strategy (aka plan) that maximizes the probability of satisfying the LTLf goal in spite of the trembling hand. We consider both deterministic and nondeterministic (adversarial) domains. We propose solution techniques for both cases by relying respectively on Markov Decision Processes and on Markov Decision Processes with Set-valued Transitions with LTLf objectives, where the set-valued probabilistic transitions capture both the nondeterminism from the environment and the possible action instruction errors from the agent. We formally show the correctness of our solution techniques and demonstrate their effectiveness experimentally through a proof-of-concept implementation.