Efficient, Safe, and Probably Approximately Complete Learning of Action Models

In this paper we explore the theoretical boundaries of planning in a setting where no model of the agent's actions is given. Instead of an action model, a set of successfully executed plans are given and the task is to generate a plan that is safe, i.e., guaranteed to achieve the goal without failing. To this end, we show how to learn a conservative model of the world in which actions are guaranteed to be applicable. This conservative model is then given to an off-the-shelf classical planner, resulting in a plan that is guaranteed to achieve the goal. However, this reduction from a model-free planning to a model-based planning is not complete: in some cases a plan will not be found even when such exists. We analyze the relation between the number of observed plans and the likelihood that our conservative approach will indeed fail to solve a solvable problem. Our analysis show that the number of trajectories needed scales gracefully

PAC Quasi-automatizability of Resolution over Restricted Distributions

We consider principled alternatives to unsupervised learning in data mining by situating the learning task in the context of the subsequent analysis task. Specifically, we consider a query-answering (hypothesis-testing) task: In the combined task, we decide whether an input query formula is satisfied over a background distribution by using input examples directly, rather than invoking a two-stage process in which (i) rules over the distribution are learned by an unsupervised learning algorithm and (ii) a reasoning algorithm decides whether or not the query formula follows from the learned rules. In a previous work (2013), we observed that the learning task could satisfy numerous desirable criteria in this combined context -- effectively matching what could be achieved by agnostic learning of CNFs from partial information -- that are not known to be achievable directly. In this work, we show that likewise, there are reasoning tasks that are achievable in such a combined context that are not known to be achievable directly (and indeed, have been seriously conjectured to be impossible, cf. (Alekhnovich and Razborov, 2008)). Namely, we test for a resolution proof of the query formula of a given size in quasipolynomial time (that is, "quasi-automatizing" resolution). The learning setting we consider is a partial-information, restricted-distribution setting that generalizes learning parities over the uniform distribution from partial information, another task that is known not to be achievable directly in various models (cf. (Ben-David and Dichterman, 1998) and (Michael, 2010))

Conditional Sparse Linear Regression

Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly identifying a significant (but perhaps small) segment of a population in which there is a highly sparse linear regression fit, together with the coefficients for the linear fit. We contend that such tasks are of interest both because the models themselves may be able to achieve better predictions in such special cases, but also because they may aid our understanding of the data. We give algorithms for such problems under the sup norm, when this unknown segment of the population is described by a k-DNF condition and the regression fit is s-sparse for constant k and s. For the variants of this problem when the regression fit is not so sparse or using expected error, we also give a preliminary algorithm and highlight the question as a challenge for future work

Implicitly Learning to Reason in First-Order Logic

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed probability distribution. PAC semantics, introduced by Valiant, is one rigorous, general proposal for learning to reason in formal languages: although weaker than classical entailment, it allows for a powerful model theoretic framework for answering queries while requiring minimal assumptions about the form of the distribution in question. To date, however, the most significant limitation of that approach, and more generally most machine learning approaches with robustness guarantees, is that the logical language is ultimately essentially propositional, with finitely many atoms. Indeed, the theoretical findings on the learning of relational theories in such generality have been resoundingly negative. This is despite the fact that first-order logic is widely argued to be most appropriate for representing human knowledge. In this work, we present a new theoretical approach to robustly learning to reason in first-order logic, and consider universally quantified clauses over a countably infinite domain. Our results exploit symmetries exhibited by constants in the language, and generalize the notion of implicit learnability to show how queries can be computed against (implicitly) learned first-order background knowledge.Comment: In Fourth International Workshop on Declarative Learning Based Programming (DeLBP 2019