Maximum Causal Entropy Specification Inference from Demonstrations

In many settings (e.g., robotics) demonstrations provide a natural way to specify tasks; however, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the tasks, such as rewards or policies, can be safely composed and/or do not explicitly capture history dependencies. Motivated by this deficit, recent works have proposed learning Boolean task specifications, a class of Boolean non-Markovian rewards which admit well-defined composition and explicitly handle historical dependencies. This work continues this line of research by adapting maximum causal entropy inverse reinforcement learning to estimate the posteriori probability of a specification given a multi-set of demonstrations. The key algorithmic insight is to leverage the extensive literature and tooling on reduced ordered binary decision diagrams to efficiently encode a time unrolled Markov Decision Process. This enables transforming a naive exponential time algorithm into a polynomial time algorithm.Comment: Computer Aided Verification, 202

The Tractability of SHAP-Score-Based Explanations over Deterministic and Decomposable Boolean Circuits

International audienceScores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential SHAPscore, a version of the Shapley value that can help explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is a computationally intractable problem, it has recently been claimed that the SHAP-score can be computed in polynomial time over the class of decision trees. In this paper, we provide a proof of a stronger result over Boolean models: the SHAP-score can be computed in polynomial time over deterministic and decomposable Boolean circuits. Such circuits, also known as tractable Boolean circuits, generalize a wide range of Boolean circuits and binary decision diagrams classes, including binary decision trees, Ordered Binary Decision Diagrams (OBDDs) and Free Binary Decision Diagrams (FBDDs). We also establish the computational limits of the notion of SHAP-score by observing that, under a mild condition, computing it over a class of Boolean models is always polynomially as hard as the model counting problem for that class. This implies that both determinism and decomposability are essential properties for the circuits that we consider, as removing one or the other renders the problem of computing the SHAP-score intractable (namely, #P-hard)

Decision diagrams in machine learning: an empirical study on real-life credit-risk data.

Decision trees are a widely used knowledge representation in machine learning. However, one of their main drawbacks is the inherent replication of isomorphic subtrees, as a result of which the produced classifiers might become too large to be comprehensible by the human experts that have to validate them. Alternatively, decision diagrams, a generalization of decision trees taking on the form of a rooted, acyclic digraph instead of a tree, have occasionally been suggested as a potentially more compact representation. Their application in machine learning has nonetheless been criticized, because the theoretical size advantages of subgraph sharing did not always directly materialize in the relatively scarce reported experiments on real-world data. Therefore, in this paper, starting from a series of rule sets extracted from three real-life credit-scoring data sets, we will empirically assess to what extent decision diagrams are able to provide a compact visual description. Furthermore, we will investigate the practical impact of finding a good attribute ordering on the achieved size savings.Advantages; Classifiers; Credit scoring; Data; Decision; Decision diagrams; Decision trees; Empirical study; Knowledge; Learning; Real life; Representation; Size; Studies;

Genetic algorithm approach to find the best input variable partitioning

Conference PaperThis paper presents a variable partition algorithm which combines the quasi-reduced ordered multiple-terminal multiple-valued decision diagrams and genetic algorithms (GAs). The algorithm is better than the previous techniques which find a good functional decomposition by non-exhaustive search and expands the range of searching for the best decomposition providing the optimal subtable multiplicity. The possible solutions are evaluated using the gain of decomposition for a multiple-output multiple-valued logic function. The distinct feature of GA is the possible solutions being coded by real numbers. Here the simplex-based crossover is proposed to use for the recombination stage of GA. It permits to increase the GA coverag

The Complexity of Reasoning with FODD and GFODD

Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and include numerical values and numerical generalizations of existential and universal quantification. Previous work presented heuristic inference algorithms for GFODDs and implemented these heuristics in systems for decision theoretic planning. In this paper, we study the complexity of the computational problems addressed by such implementations. In particular, we study the evaluation problem, the satisfiability problem, and the equivalence problem for GFODDs under the assumption that the size of the intended model is given with the problem, a restriction that guarantees decidability. Our results provide a complete characterization placing these problems within the polynomial hierarchy. The same characterization applies to the corresponding restriction of problems in first order logic, giving an interesting new avenue for efficient inference when the number of objects is bounded. Our results show that for $\Sigma_k$ formulas, and for corresponding GFODDs, evaluation and satisfiability are $\Sigma_k^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete. For $\Pi_k$ formulas evaluation is $\Pi_k^p$ complete, satisfiability is one level higher and is $\Sigma_{k+1}^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete.Comment: A short version of this paper appears in AAAI 2014. Version 2 includes a reorganization and some expanded proof