Multiobjective Preexpectation Reasoning for Probabilistic Programs

2026-08-13

AI Summary

This work addresses the problem of multi-objective expected reward optimization in infinite-state Markov decision processes, aiming to synthesize policies that approximate the Pareto front. To this end, it introduces the first deductive program-level reasoning framework that integrates multi-objective optimization with weak expectation semantics. The approach features a novel multi-objective expectation transformer and employs a convex hull power domain to symbolically represent post-expectation tuples. By combining hybrid determinization rules for policy synthesis with operational semantics modeling, the method enables symbolic policy synthesis over infinite state spaces. Experimental evaluation demonstrates its effectiveness in solving multi-objective optimization problems across several case studies.

Abstract

Probabilistic programs with nondeterminism model planning problems in which a strategy resolves the nondeterminism to optimize an expected outcome. We study the multiobjective setting, optimizing several outcomes at once along a Pareto front, and provide a deductive, program-level account of strategy synthesis. Its core is a multiobjective preexpectation transformer mapping a tuple of postexpectations to the set of simultaneously achievable values, an element of the convex Hoare powerdomain. It conservatively extends weakest preexpectations and lifts standard loop rules. We develop rules to synthesize witnessing strategies as mixed determinizations that randomize over non-probabilistic determinizations. We prove the transformer and synthesis rules sound against an operational MDP semantics, without requiring a finite state space: our approach can be seen as a symbolic approach - at program level - for multiobjective optimization over infinite MDPs. We demonstrate our machinery using various case studies.

Problem

• multiobjective optimization
• probabilistic programs
• nondeterminism
• strategy synthesis
• Pareto front

Innovation

• multiobjective preexpectation
• probabilistic programs
• strategy synthesis
• convex Hoare powerdomain
• symbolic optimization