In this paper we compare the abstraction methods used for state space search and planning in Artificial Intelligence with the state space relaxation methods used in Operations Research for various optimization problems such as the Travelling Salesman problem (TSP). Although developed independently, these methods are based on exactly the same general idea: lower bounds on distances in a given state space can be derived by computing exact distances in a ``simplified" state space. Our aim is to describe these methods so that the two communities understand what each other has done and can begin to work together.

Optimization-based heuristics may offer very good estimates. But, calculatingthem may be time consuming, especially if the optimization problem isintractable. This raises the question of their applicability. This papersummarizes early work from the year 2000 on optimization-based heuristics inthe context of PDBs for the Tile-Puzzle. We show that an admissible heuristicbased on Vertex-Cover (VC) can be calculated in reasonable time over a largecollection of small PDBs. When larger PDBs are involved we suggest the idea ofusing another lookup table that precalculates and stores all possible relevantVC values. This table can be later looked up in a constant time during thesearch. We discuss the conditions under which this idea can be generalized.Experimental results demonstrate the applicability of these two ideas on the15- and 24-Puzzle. The first idea appeared in (Felner, Korf and Hanan, 2004) but the secondidea is presented here for the first time.

Stochastic Physical Search (SPS) refers to the search for an item in a physical environment where the item's price is stochastic, and where the cost to obtain the item includes both travel and purchase costs. This type of problem models task planning scenarios where the cost of completing an objective at a location is drawn from a probability distribution, reflecting the influence of unknown factors. Prior work on this domain has focused on solutions where the expected cost is minimized. Recently, SPS problems with other objectives have been proposed and theoretically analyzed, in particular when either the budget or the desired probability of success is fixed. However, general optimal solvers for these new variants do not yet exist. We present algorithms for optimal solution of these variants on general graphs. We formulate them as mixed integer linear programming problems, and solve them using an off-the-shelf MILP solver. We then develop custom branch and bound algorithms which result in a dramatic reduction in computation speed. Using these algorithms, we generate empirical insights into the hardness landscape of the fixed budget and fixed probability of success SPS variants.

We consider the problem of indoor human trajectory identification using odometry data from smartphone sensors. Given a segmented trajectory, a simplified map of the environment, and a set of error thresholds, we implement a map-matching algorithm in a urban setting and analyze the accuracy of the resulting path. We also discuss aggregation of user step data into a segmented trajectory. Besides providing an interesting application of learning human motion in a constrained environment, we examine how the uncertainty of the snapped trajectory varies with path length. We demonstrate that as new segments are added to a path, the number of possibilities for earlier segments decreases monotonically. Applications of this work in an urban setting are discussed, as well as future plans to develop a formal theory of odometry-based map-matching.

Learning to provide appropriate assistance to people indifferent situations is an extremely important, but insufficientlyinvestigated machine learning task. Applications includehuman-robot and human-computer interactions settings to maximizing the benefits of assistive technologies. Three key challenges must be overcome to appropriately address this task: Complexity: the space of possible assistive policies can be very large, making many existing methods (e.g., fromreinforcement learning) too data inefficient to be practical. Noise and misspecification: observed human behavior is often noisy and parametric formulations that reduce complexity will typically suffer from model misspecification,leading to unboundedly sub-optimal assistance. Biasedness: data available for learning a model is biased by previously provided assistive actions, violating the typical assumptions of supervised learning. We develop a general framework for learning to assist in single intervention settings. The framework narrows the search for effective assistance by viewing previous behavior under assistance through a restricted set of statistics. Assistive policies for the worst-case context-assistance-outcome relationships satisfying these statistics are obtained. We embed the problem of learning how to assist users in cursor based target pointing tasks into this framework and outline its usage.

Algorithm portfolios seek to determine an effective set of algorithms that can be used within an algorithm selection framework to solve problems. A limited number of these portfolio studies focus on generating different versions of a target algorithm using different parameter configurations. In this paper, we employ a Design of Experiments (DOE) approach to determine a promising range of values for each parameter of an algorithm. These ranges are further processed to determine a portfolio of parameter configurations, which would be used within two online Algorithm Selection approaches for solving different instances of a given combinatorial optimization problem effectively. We apply our approach on a Simulated Annealing-Tabu Search (SA-TS) hybrid algorithm for solving the Quadratic Assignment Problem (QAP) as well as an Iterated Local Search (ILS) on the Travelling Salesman Problem (TSP). We also generate a portfolio of parameter configurations using best-of-breed parameter tuning approaches directly for the comparison purpose. Experimental results show that our approach lead to improvements over best-of-breed parameter tuning approaches.

We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision tasks. We are not satisfied with just guaranteeing minimax regret rates, but we want our algorithms to perform significantly better on easy data. Two popular ways to formalize such adaptivity are second-order regret bounds and quantile bounds. The underlying notions of 'easy data', which may be paraphrased as "the learning problem has small variance" and "multiple decisions are useful", are synergetic. But even though there are sophisticated algorithms that exploit one of the two, no existing algorithm is able to adapt to both. In this paper we outline a new method for obtaining such adaptive algorithms, based on a potential function that aggregates a range of learning rates (which are essential tuning parameters). By choosing the right prior we construct efficient algorithms and show that they reap both benefits by proving the first bounds that are both second-order and incorporate quantiles.

Motivated by the task of hyperparameter optimization, we introduce the non-stochastic best-arm identification problem. Within the multi-armed bandit literature, the cumulative regret objective enjoys algorithms and analyses for both the non-stochastic and stochastic settings while to the best of our knowledge, the best-arm identification framework has only been considered in the stochastic setting. We introduce the non-stochastic setting under this framework, identify a known algorithm that is well-suited for this setting, and analyze its behavior. Next, by leveraging the iterative nature of standard machine learning algorithms, we cast hyperparameter optimization as an instance of non-stochastic best-arm identification, and empirically evaluate our proposed algorithm on this task. Our empirical results show that, by allocating more resources to promising hyperparameter settings, we typically achieve comparable test accuracies an order of magnitude faster than baseline methods.

Finding satisfying assignments for the variables involved in a set of constraints can be cast as a (bounded) model generation problem: search for (bounded) models of a theory in some logic. The state-of-the-art approach for bounded model generation for rich knowledge representation languages like ASP and FO(.) and a CSP modeling language such as Zinc, is ground-and-solve: reduce the theory to a ground or propositional one and apply a search algorithm to the resulting theory. An important bottleneck is the blow-up of the size of the theory caused by the grounding phase. Lazily grounding the theory during search is a way to overcome this bottleneck. We present a theoretical framework and an implementation in the context of the FO(.) knowledge representation language. Instead of grounding all parts of a theory, justifications are derived for some parts of it. Given a partial assignment for the grounded part of the theory and valid justifications for the formulas of the non-grounded part, the justifications provide a recipe to construct a complete assignment that satisfies the non-grounded part. When a justification for a particular formula becomes invalid during search, a new one is derived; if that fails, the formula is split in a part to be grounded and a part that can be justified. Experimental results illustrate the power and generality of this approach.

We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax lower bounds (up to log factors), showing that under certain assumptions, our algorithm is information-theoretically optimal. Our results represent the first tractable algorithm guaranteeing successful recovery with tight bounds on recovery errors and sample complexity.