Guiding SMT solvers with Monte Carlo Tree Search and neural networks

Stéphane Graham-Lengrand (1, 2) , Michael Färber (3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 PARSIFAL - Proof search and reasoning with logic specifications
3 Universität Innsbruck [Innsbruck]

Monte Carlo Tree Search (MCTS) is a technique to guide search in a large decision space by taking random samples and evaluating their outcome. Frequently, MCTS is employed together with reward heuristics learnt by neural networks. The talk will propose a guidance mechanism for SMT solvers based on a combination of MCTS and neural networks. Machine learning methods gain importance in automated reasoning. A particularly strong trend are neural networks, having produced state-of-the-art results for premise selection [WTWD17, ISA + 16]. Outside of automated reasoning, neural networks have been combined with Monte Carlo Tree Search, treating problems as diverse as finding good strategies to play the game of Go [SHM + 16] and planning of chemical syntheses [SKTW17, SPW17]. In automated reasoning, Monte Carlo Tree Search (MCTS) has been applied to first-order automated theorem proving, using hand-crafted heuristics instead of neural networks [FKU17]. We propose a combination of Monte Carlo Tree Search and neural networks to guide the search performed by an SMT solver. We are exploring the idea of such guidance in the Psyche platform [GL13], which offers a modular architecture for theorem proving. It implements an adaptation, to automated reasoning in general and to SMT solving in particular, of the LCF architecture [Mil79, GMW79]. LCF is mostly used in Interactive Theorem Proving and is particualrly widely implemented in the proof assistants of the HOL family, such as the HOL system [HOL], Isabelle [Isa], etc. The LCF architecture allows theorem proving strategies to be programmable, while guaranteeing the correctness of any claim that a formula is provable. The architecture's kernel component offers an API whose primitives implement basic reasoning inferences, and strategies can be programmed on top of the kernel via the API. The claims of provability are then necessarily correct-by-construction, assuming the correctness of the kernel, but regardless of any potential defects in the design or in the implementation of strategies (or in the user's input, for the case of Interactive Theorem Proving). Psyche embraces this paradigm and, in the case of SMT solving, relates to a position paper by de Moura and Passmore, entitled "The strategy challenge in SMT solving" [dMP13], which promoted the programmability of strategies as compositions of basic reasoning tasks, explicitly referring to the LCF paradigm. This approach opens up the possibilities of extensively experimenting with various strategies, whether they be handcrafted or machine-learned, while never jeopardising the correctness of the solver's output. Guiding the search by techniques such as MCTS and neural networks can be envisaged more easily in provers whose architecture implements this approach. Psyche's architecture does so at a rather fine-grained level, separating the code that implements reasoning inferences from the code that implements search strategies.

Domaines: Logique en informatique [cs.LO]; Intelligence artificielle [cs.AI]

Stéphane Graham-Lengrand, Michael Färber. Guiding SMT solvers with Monte Carlo Tree Search and neural networks. Third Conference on Artificial Intelligence and Theorem Proving (AITP'2018), Mar 2018, Aussois, France. ⟨hal-01935578⟩