The Computational Complexity of Probabilistic Planning

Abstract

We examine the computational complexity of testing and nding small plans in probabilistic planning domains with both at and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural de nitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, co-NP, PP, N P PP , co-NP PP , and PSPACE. In the process of proving that certain planning problems are complete for NP PP , w e i n troduce a new basic NP PP -complete problem, E-Majsat, which generalizes the standard Boolean satis ability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for E-Majsat could be important for the creation of e cient algorithms for a wide variety of problems.

Functional Representation of Prototypes in LVQ and Relevance Learning

“…Results are shown in Tables 1, 2, and 3. The table 1 reveals slight over-fitting in our models since it did not generalize well when compared to the baselines, i.e., we seem to obtain better accuracy on the training data than the authors in [26] while their system generalize better on unseen data. However, observing deeply, we see only slight variations between train and test accuracy.…”

“…Tables 1, 2 and 3 display the results obtained on the datasets used. For table 1, we used the results from Rocktaschel et al, [26], Baudis et al, [2] and Bowman et al, [9] as the baseline systems on SNLI and SICK respectively. For PASCAL-RTE3, we did not include any baseline system since there is no recent work which use similar deep learning approach on that dataset.…”

“…In particular, the authors in [26] using attention-based LSTM have reported state of the art results in textual entailment.…”

“…The authors in [26] proposed a word-by-word neural attention mechanism based on LSTM. The idea is to have two LSTMs, one reasoning over the sequence of tokens in the text while the other is reasoning on the hypothesis sequence.…”

Task Planning for an Autonomous Service Robot

“…These approaches try to generate conditional plans and policies (mappings from states to actions), respectively. Unfortunately, both approaches are of much higher complexity [7,8] than classical planning and usually fail to scale in even moderately complex scenarios. Furthermore, it might be impossible to model all potential outcomes of actions in dynamic environments, or concrete probabilities of outcomes are unknown.…”