William Cushing

Planar graphs are 1-relaxed, 4-choosable

We show that every planar graph G=(V,E) is 1-relaxed, 4-choosable. This means that, for every list assignment L that assigns a set of at least four colors to each vertex, there exists a coloring f such that f(v)@?L(v) for every vertex v@?V and each color class f^-^1(@a) of f induces a subgraph with maximum degree at most 1.

Learning Probabilistic Hierarchical Task Networks as Probabilistic Context-Free Grammars to Capture User Preferences

We introduce an algorithm to automatically learn probabilistic hierarchical task networks (pHTNs) that capture a users preferences on plans by observing only the users behavior. HTNs are a common choice of representation for a variety of purposes in planning, including work on learning in planning. Our contributions are twofold. First, in contrast with prior work, which employs HTNs to represent domain physics or search control knowledge, we use HTNs to model user preferences. Second, while most prior work on HTN learning requires additional information (e.g., annotated traces or tasks) to assist the learning process, our system only takes plan traces as input. Initially, we will assume that users carry out preferred plans more frequently, and thus the observed distribution of plans is an accurate representation of user preference. We then generalize to the situation where feasibility constraints frequently prevent the execution of preferred plans. Taking the prevalent perspective of viewing HTNs as grammars over primitive actions, we adapt an expectation-maximization (EM) technique from the discipline of probabilistic grammar induction to acquire probabilistic context-free grammars (pCFG) that capture the distribution on plans. To account for the difference between the distributions of possible and preferred plans, we subsequently modify this core EM technique by rescaling its input. We empirically demonstrate that the proposed approaches are able to learn HTNs representing user preferences better than the inside-outside algorithm. Furthermore, when feasibility constraints are obfuscated, the algorithm with rescaled input performs better than the algorithm with the original input.

State agnostic planning graphs: deterministic, non-deterministic, and probabilistic planning

Planning graphs have been shown to be a rich source of heuristic information for many kinds of planners. In many cases, planners must compute a planning graph for each element of a set of states, and the naive technique enumerates the graphs individually. This is equivalent to solving a multiple-source shortest path problem by iterating a single-source algorithm over each source. We introduce a data-structure, the state agnostic planning graph, that directly solves the multiple-source problem for the relaxation introduced by planning graphs. The technique can also be characterized as exploiting the overlap present in sets of planning graphs. For the purpose of exposition, we first present the technique in deterministic (classical) planning to capture a set of planning graphs used in forward chaining search. A more prominent application of this technique is in conformant and conditional planning (i.e., search in belief state space), where each search node utilizes a set of planning graphs; an optimization to exploit state overlap between belief states collapses the set of sets of planning graphs to a single set. We describe another extension in conformant probabilistic planning that reuses planning graph samples of probabilistic action outcomes across search nodes to otherwise curb the inherent prediction cost associated with handling probabilistic actions. Finally, we show how to extract a state agnostic relaxed plan that implicitly solves the relaxed planning problem in each of the planning graphs represented by the state agnostic planning graph and reduces each heuristic evaluation to counting the relevant actions in the state agnostic relaxed plan. Our experimental evaluation (using many existing International Planning Competition problems from classical and non-deterministic conformant tracks) quantifies each of these performance boosts, and demonstrates that heuristic belief state space progression planning using our technique is competitive with the state of the art.