Ensuring Logic in the Fog: Sound POMDP Synthesis with LTL Objectives

Partially Observable Markov Decision Processes (POMDPs) are the standard framework for decision-making under uncertainty. While sampling-based methods scale well, they lack formal correctness guarantees, making them unsuitable for safety-critical applications. Conversely, formal synthesis techniques provide correctness-by-construction but often struggle with scalability, as general POMDP synthesis is undecidable. To bridge this gap, we propose a synthesis framework that integrates sampling, automata learning, and model-checking. Inspired by Angluin's $L^*$ algorithm, our approach utilizes sampling as a membership oracle and model-checking as an equivalence oracle. This enables the synthesis of finite-state controllers with formal guarantees, provided the sampling-induced policy is regular. We establish a relative completeness result for this framework. Experimental results from our prototypical implementation demonstrate that this method successfully solves threshold-safety problems that remain challenging for existing formal synthesis tools. We believe our algorithm serves as a valuable component in a portfolio approach to tackling the inherent difficulty of POMDP synthesis problems.

Strategy synthesis typically follows an all-or-nothing paradigm, returning unrealisable whenever a specification cannot be guaranteed in an uncertain environment. In this paper, we introduce optimal LTLf synthesis, where the goal is to realise as many objectives as possible from a given specification consisting of multiple objectives, especially for the case that they are not all jointly realisable. We first consider max-guarantee synthesis, which commits to a maximal set of objectives that we can a priori guarantee to realise. We then introduce max-observation synthesis, which maximises a posteriori realised objectives that may be incomparable on different executions. Finally, we present incremental max-observation synthesis, which further improves strategies by exploiting opportunities for stronger guarantees when they arise during an execution. Experimental results show that different variations of optimal synthesis scale broadly equally well, solving a large fraction of the benchmark instances within the given timeout, demonstrating the practical feasibility of the approach.

This paper addresses key technical challenges in current large language model (LLM) agent applications, including long-horizon planning, sparse reward attribution, and dynamic environmental interaction, by designing and optimizing an intelligent agent workflow. The proposed architecture is based on the synthesis of core AI paradigms: Visual, Language, Generative, Graph, Multimodal, Reinforcement, and Agent Intelligence. Unlike conventional baseline models that rely on static prompting and lack robust perception-action loops, our approach introduces a Partially Observable Markov Decision Process (POMDP) routing mechanism. This mechanism is augmented with an internal, self-correcting reward model that evaluates decision trajectories before execution. By integrating multimodal inputs and advanced reinforcement learning principles (such as proximal policy optimization and value function approximation), the agent maintains long-term structural memory and dynamically adapts its reasoning pathways to mitigate error accumulation. Empirical experiments on the ALFWorld embodied simulation environment and the WebShop online navigation benchmark demonstrate a 24.5% absolute improvement in task success rate and trajectory efficiency over mainstream baselines like the standard ReAct framework. Comprehensive ablation studies confirm the significant contribution of the reward-driven critique module in suppressing hallucination rates. This research bridges theoretical foundations of reinforcement learning and graph-based memory with autonomous agent workflows. Ultimately, the resulting architecture offers a practical, scalable reference framework for developing artificial intelligence technologies in complex, multi-step autonomous systems. Code is available at https://github.com/01Amez/RLAW_Implementation.