The Eos SMT/SMA-solver: a preliminary report

This is a preliminary report of work in progress on the development of the Eos SMT/SMA-solver. Eos is the first solver built from the start based on the CDSAT (Conflict-Driven SATisfiability) paradigm for solving satisfiability problems modulo theories and assignments. The latter means that assignments to first-order terms may appear in the input. CDSAT generalizes MCSAT (Model-Constructing SATisfiability), hence CDCL (Conflict-Driven Clause Learning), to theory combination. CDSAT reasons in a union of theories by combining in a conflict-driven manner theory inference systems, called theory modules. The current version of Eos has modules for propositional logic, equality with uninterpreted function symbols (UF), and linear real arithmetic. The module for propositional logic is a MiniSAT-inspired SAT solver. A key feature of MCSAT/CDSAT is theory conflict explanation by theory inferences: to this end, the Eos module for UF applies congruence closure inferences, and the Eos module for real arithmetic uses Fourier-Motzkin resolution; both rules may generate new (i.e., non-input) literals. The core solver in Eos implements the CDSAT transition system and several heuristics used in state-of-the-art CDCL-based SAT solvers. Some of these heuristics (e.g., random restarts) can be reused directly in the context of CDSAT, while others are adapted. Eos employs a generalization of the VSIDS heuristics to make decisions on both propositional and first-order terms, and the watched literals scheme for both BCP (Boolean Constraint Propagation) and deductions involving arithmetic terms and uninterpreted terms

Risk-aware shielding of Partially Observable Monte Carlo Planning policies

Partially Observable Monte Carlo Planning (POMCP) is a powerful online algorithm that can generate approximate policies for large Partially Observable Markov Decision Processes. The online nature of this method supports scalability by avoiding complete policy representation. However, the lack of an explicit policy representation hinders interpretability and a proper evaluation of the risks an agent may incur. In this work, we propose a methodology based on Maximum Satisfiability Modulo Theory (MAX-SMT) for analyzing POMCP policies by inspecting their traces, namely, sequences of belief- action pairs generated by the algorithm. The proposed method explores local properties of the policy to build a compact and informative summary of the policy behaviour. Moreover, we introduce a rich and formal language that a domain expert can use to describe the expected behaviour of a policy. In more detail, we present a formulation that directly computes the risk involved in taking actions by considering the high- level elements specified by the expert. The final formula can identify risky decisions taken by POMCP that violate the expert indications. We show that this identification process can be used offline (to improve the policy’s explainability and identify anomalous behaviours) or online (to shield the risky decisions of the POMCP algorithm). We present an extended evaluation of our approach on four domains: the well-known tiger and rocksample benchmarks, a problem of velocity regulation in mobile robots, and a problem of battery management in mobile robots. We test the methodology against a state-of- the-art anomaly detection algorithm to show that our approach can be used to identify anomalous behaviours in faulty POMCP. We also show, comparing the performance of shielded and unshielded POMCP, that the shielding mechanism can improve the system’s performance. We provide an open-source implementation of the proposed methodologies at https://github.com/GiuMaz/XPOMCP

Rule-Based Policy Interpretation and Shielding for Partially Observable Monte Carlo Planning

Partially Observable Monte Carlo Planning (POMCP) is a powerful online algorithm that can generate approximate policies for large Partially Observable Markov Decision Processes. The online nature of this method supports scalability by avoiding complete policy representation. However, the lack of an explicit representation of the policy hinders interpretability. In this thesis, we propose a methodology based on Maximum Satisfiability Modulo Theory (MAX-SMT) for analyzing POMCP policies by inspecting their traces, namely, sequences of belief-action pairs generated by the algorithm. The proposed method explores local properties of the policy to build a compact and informative summary of the policy behaviour. This representation exploits a high-level description encoded using logical formulas that domain experts can provide. The final formula can be used to identify unexpected decisions, namely, decisions that violate the expert indications. We show that this identification process can be used offline (to improve the explainability of the policy and to identify anomalous behaviours) or online (to shield the decisions of the POMCP algorithm). We also present an active methodology that can effectively query a POMCP policy to build more reliable descriptions quickly. We extensively evaluate our methodologies on two standard benchmarks for POMDPs, namely, emph{tiger} and emph{rocksample}, and on a problem related to velocity regulation in mobile robot navigation. Results show that our approach achieves good performance due to its capability to exploit experts' knowledge of the domains. Specifically, our approach can be used both to identify anomalous behaviours in faulty POMCPs and to improve the performance of the system by using the shielding mechanism. In the first case, we test the methodology against a state-of-the-art anomaly detection algorithm, while in the second, we compared the performance of shielded and unshielded POMCPs. We implemented our methodology in CC, and the code is open-source and available at href{https://github.com/GiuMaz/XPOMCP}{https://github.com/GiuMaz/XPOMCP}

Rule-based Shield Synthesis for Partially Observable Monte Carlo Planning

Partially Observable Monte-Carlo Planning (POMCP) is a powerful online algorithm able to generate approximate policies for large Partially Observable Markov Decision Processes. The online nature of this method supports scalability by avoiding complete policy representation. The lack of an explicit representation however hinders policy interpretability and makes policy verification very complex. In this work, we propose two contributions. The first is a method for identifying unexpected actions selected by POMCP with respect to expert prior knowledge of the task. The second is a shielding approach that prevents POMCP from selecting unexpected actions. The first method is based on Maximum Satisfiability Modulo Theory (MAX-SMT). It inspects traces (i.e., sequences of belief-action-observation triplets) generated by POMCP to compute the parameters of logical formulas about policy properties defined by the expert. The second contribution is a module that uses online the logical formulas to identify anomalous actions selected by POMCP and substitutes those actions with actions that satisfy the logical formulas fulfilling expert knowledge. We evaluate our approach in two domains. Results show that the shielded POMCP outperforms the standard POMCP in a case study in which a wrong parameter of POMCP makes it select wrong actions from time to time. © 2021 Copyright for this paper by its authors

Rule-based shielding for Partially Observable Monte-Carlo Planning

Partially Observable Monte-Carlo Planning (POMCP) is a powerful online algorithm able to generate approximate policies for large Partially Observable Markov Decision Processes. The online nature of this method supports scalability by avoiding complete policy representation. The lack of an explicit representation however hinders policy interpretability and makes policy verification very complex. In this work, we propose two contributions. The first is a method for identifying unexpected actions selected by POMCP with respect to expert prior knowledge of the task. The second is a shielding approach that prevents POMCP from selecting unexpected actions. The first method is based on Satisfiability Modulo Theory (SMT). It inspects traces (i.e., sequences of belief-action-observation triplets) generated by POMCP to compute the parameters of logical formulas about policy properties defined by the expert. The second contribution is a module that uses online the logical formulas to identify anomalous actions selected by POMCP and substitutes those actions with actions that satisfy the logical formulas fulfilling expert knowledge. We evaluate our approach on Tiger, a standard benchmark for POMDPs, and a real-world problem related to velocity regulation in mobile robot navigation. Results show that the shielded POMCP outperforms the standard POMCP in a case study in which a wrong parameter of POMCP makes it select wrong actions from time to time. Moreover, we show that the approach keeps good performance also if the parameters of the logical formula are optimized using trajectories containing some wrong actions

Identification of Unexpected Decisions in Partially Observable Monte-Carlo Planning: a Rule-Based Approach

Partially Observable Monte-Carlo Planning (POMCP) is a powerful online algorithm able to generate approximate policies for large Partially Observable Markov Decision Processes. The online nature of this method supports scalability by avoiding complete policy representation. The lack of an explicit representation however hinders interpretability. In this work, we propose a methodology based on Satisfiability Modulo Theory (SMT) for analyzing POMCP policies by inspecting their traces, namely sequences of belief-action-observation triplets generated by the algorithm. The proposed method explores local properties of policy behavior to identify unexpected decisions. We propose an iterative process of trace analysis consisting of three main steps, i) the definition of a question by means of a parametric logical formula describing (probabilistic) relationships between beliefs and actions, ii) the generation of an answer by computing the parameters of the logical formula that maximize the number of satisfied clauses (solving a MAX-SMT problem), iii) the analysis of the generated logical formula and the related decision boundaries for identifying unexpected decisions made by POMCP with respect to the original question. We evaluate our approach on Tiger, a standard benchmark for POMDPs, and a real-world problem related to mobile robot navigation. Results show that the approach can exploit human knowledge on the domain, outperforming state-of-the-art anomaly detection methods in identifying unexpected decisions. An improvement of the Area Under Curve up to 47\% has been achieved in our tests.Comment: AAMAS 2021, 3-7 May 2021, London-UK (Virtual

Learning logic specifications for soft policy guidance in POMCP

Partially Observable Monte Carlo Planning (POMCP) is an effi- cient solver for Partially Observable Markov Decision Processes (POMDPs). It allows scaling to large state spaces by computing an approximation of the optimal policy locally and online, using a Monte Carlo Tree Search based strategy. However, POMCP suffers from sparse reward function, namely, rewards achieved only when the final goal is reached, particularly in environments with large state spaces and long horizons. Recently, logic specifications have been integrated into POMCP to guide exploration and to satisfy safety requirements. However, such policy-related rules require manual definition by domain experts, especially in real-world sce- narios. In this paper, we use inductive logic programming to learn logic specifications from traces of POMCP executions, i.e., sets of belief-action pairs generated by the planner. Specifically, we learn rules expressed in the paradigm of answer set programming. We then integrate them inside POMCP to provide soft policy bias toward promising actions. In the context of two benchmark sce- narios, rocksample and battery, we show that the integration of learned rules from small task instances can improve performance with fewer Monte Carlo simulations and in larger task instances. We make our modified version of POMCP publicly available at https://github.com/GiuMaz/pomcp_clingo.git

Social cost of chronic pain in Italy

Chronic pain negatively impacts on sick people's daily life and their working ability, and it is a heavy financial burden on the health systems. This article is aimed at evaluating the social costs of chronic pain in Italy.The analysis is based on national tariffs and prices and on epidemiologic, health resource consumption, and absence from work published data; when no information specifically related to Italy was available, results from studies carried out in other European Countries were used as appropriate.The average annual cost per patient amounts to €4,556, 31% of which (€1,400) is charged on the National Health Service. Of this share, 51% is due to hospitalisation and 6% to analgesic drug (mostly NSAIDs) costs. Indirect costs (€3,157) are caused by sickness leaves (31%) and retirements.Based on an estimated prevalence of 8 million people with pain in Italy, the impact of chronic pain direct costs on public health expenditure results 9.6%, whereas the impact of total costs on gross domestic product..

From POMDP executions to policy specifications

Partially Observable Markov Decision Processes (POMDPs) allow modeling systems with uncertain state using probability distributions over states (called beliefs). However, in complex domains, POMDP solvers must explore large belief spaces, which is computationally intractable. One solution is to introduce domain knowledge to drive exploration, in the form of logic specifications. However, defining effective specifications may be challenging even for domain experts. We propose an approach based on inductive logic programming to learn specifications with confidence level from observed POMDP executions. We show that the learning approach converges to robust specifications as the number of examples increases