While in classical planning the objective is to achieve one of the equally attractive goal states at as low total action cost as possible, the objective in deterministic oversubscription planning (OSP) is to achieve an as valuable as possible subset of goals within a fixed allowance of the total action cost. Although numerous applications in various fields share the latter objective, no substantial algorithmic advances have been made in deterministic OSP. Tracing the key sources of progress in classical planning, we identify a severe lack of effective domain-independent approximations for OSP.With our focus here on optimal planning, our goal is to bridge this gap. Two classes of approximation techniques have been found especially useful in the context of optimal classical planning: those based on state-space abstractions and those based on logical landmarks for goal reachability. The question we study here is whether some similar-in-spirit, yet possibly mathematically different, approximation techniques can be developed for OSP. In the context of abstractions, we define the notion of additive abstractions for OSP, study the complexity of deriving effective abstractions from a rich space of hypotheses, and reveal some substantial, empirically relevant islands of tractability. In the context of landmarks, we show how standard goal-reachability landmarks of certain classical planning tasks can be compiled into the OSP task of interest, resulting in an equivalent OSP task with a lower cost allowance, and thus with a smaller search space. Our empirical evaluation confirms the effectiveness of the proposed techniques, and opens a wide gate for further developments in oversubscription planning.

In deterministic OSP, the objective is to achieve an as valuable as possible subset of goals within a fixed allowance of the total action cost. Although numerous applications in various fields share this objective, no substantial algorithmic advances have been made beyond the very special settings of net-benefit optimization. Tracing the key sources of progress in classical planning, we identify a severe lack of domain-independent approximations for OSP, and start with investigating the prospects of abstraction approximations for this problem. In particular, we define the notion of additive abstractions for OSP, study the complexity of deriving effective abstractions from a rich space of hypotheses, and reveal some  substantial, empirically relevant islands of tractability.

Predicting the answer to a product-related question is an emerging field of research that recently attracted a lot of attention. Answering subjective and opinion-based questions is most challenging due to the dependency on customer-generated content. Previous works mostly focused on review-aware answer prediction; however, these approaches fail for new or unpopular products, having no (or only a few) reviews at hand. In this work, we propose a novel and complementary approach for predicting the answer for such questions, based on the answers for similar questions asked on similar products. We measure the contextual similarity between products based on the answers they provide for the same question. A mixture-of-expert framework is used to predict the answer by aggregating the answers from contextually similar products. Empirical results demonstrate that our model outperforms strong baselines on some segments of questions, namely those that have roughly ten or more similar resolved questions in the corpus. We additionally publish two large-scale datasets 1 used in this work, one is of similar product question pairs, and the second is of product question-answer pairs. * Work carried out during an internship at Amazon. † Work carried out while working at Amazon.

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Problem abstractions based on (either completely or partially) ignoring delete effects of the actions provide the basis for some seminal classical planning heuristics. However, the palette of the conceptual tools exploited by these heuristics remains rather limited. We study a framework for approximating the optimal cost solutions for problems with no delete effects that bridges between certain works on heuristic-search classical planning and on probabilistic reasoning. Our analysis results in developing a novel heuristic function that combines "informed" setstructured cost estimates and "conservative" action cost sharing. Our empirical comparative evaluation provides a clear evidence for the attractiveness of this heuristic estimate. In addition, we examine a (suggested before in the context of probabilistic reasoning) admissible heuristic based on a stronger variant of action cost sharing. We show that what is good for "typical" problems of probabilistic reasoning turns out not to be so for "typical" problems of classical planning, and provide a formal account for that difference.