What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical system to compute based on this notion. It proposes a behavioural characterisation of computing in terms of a measure of programmability, which reflects a system's ability to react to external stimuli. The proposed measure of programmability is useful for classifying computers in terms of the apparent algorithmic complexity of their evolution in time. I make some specific proposals in this connection and discuss this approach in the context of other behavioural approaches, notably Turing's test of machine intelligence. I also anticipate possible objections and consider the applicability of these proposals to the task of relating abstract computation to nature-like computation.

The outlying property detection problem is the problem of discovering the properties distinguishing a given object, known in advance to be an outlier in a database, from the other database objects. In this paper, we analyze the problem within a context where numerical attributes are taken into account, which represents a relevant case left open in the literature. We introduce a measure to quantify the degree the outlierness of an object, which is associated with the relative likelihood of the value, compared to the to the relative likelihood of other objects in the database. As a major contribution, we present an efficient algorithm to compute the outlierness relative to significant subsets of the data. The latter subsets are characterized in a "rule-based" fashion, and hence the basis for the underlying explanation of the outlierness.

We consider how selfish agents are likely to share revenues derived from maintaining connectivity between important network servers. We model a network where a failure of one node may disrupt communication between other nodes as a cooperative game called the vertex Connectivity Game (CG). In this game, each agent owns a vertex, and controls all the edges going to and from that vertex. A coalition of agents wins if it fully connects a certain subset of vertices in the graph, called the primary vertices. Power indices measure an agent's ability to affect the outcome of the game. We show that in our domain, such indices can be used to both determine the fair share of the revenues an agent is entitled to, and identify significant possible points of failure affecting the reliability of communication in the network. We show that in general graphs, calculating the Shapley and Banzhaf power indices is #P-complete, but suggest a polynomial algorithm for calculating them in trees. We also investigate finding stable payoff divisions of the revenues in CGs, captured by the game theoretic solution of the core, and its relaxations, the epsilon-core and least core. We show a polynomial algorithm for computing the core of a CG, but show that testing whether an imputation is in the epsilon-core is coNP-complete. Finally, we show that for trees, it is possible to test for epsilon-core imputations in polynomial time.

In this article we introduce the Arcade Learning Environment (ALE): both a challenge problem and a platform and methodology for evaluating the development of general, domain-independent AI technology. ALE provides an interface to hundreds of Atari 2600 game environments, each one different, interesting, and designed to be a challenge for human players. ALE presents significant research challenges for reinforcement learning, model learning, model-based planning, imitation learning, transfer learning, and intrinsic motivation. Most importantly, it provides a rigorous testbed for evaluating and comparing approaches to these problems. We illustrate the promise of ALE by developing and benchmarking domain-independent agents designed using well-established AI techniques for both reinforcement learning and planning. In doing so, we also propose an evaluation methodology made possible by ALE, reporting empirical results on over 55 different games. All of the software, including the benchmark agents, is publicly available.

The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice. While these relaxations can be solved globally optimally, they are often too loose and thus lead to results far away from the optimum. In this paper we show that every constrained minimization problem of a ratio of non-negative set functions allows a tight relaxation into an unconstrained continuous optimization problem. This result leads to a flexible framework for solving constrained problems in network analysis. While a globally optimal solution for the resulting non-convex problem cannot be guaranteed, we outperform the loose convex or spectral relaxations by a large margin on constrained local clustering problems.

Most of the existing methods for sparse signal recovery assume a static system: the unknown signal is a finite-length vector for which a fixed set of linear measurements and a sparse representation basis are available and an L1-norm minimization program is solved for the reconstruction. However, the same representation and reconstruction framework is not readily applicable in a streaming system: the unknown signal changes over time, and it is measured and reconstructed sequentially over small time intervals. In this paper, we discuss two such streaming systems and a homotopy-based algorithm for quickly solving the associated L1-norm minimization programs: 1) Recovery of a smooth, time-varying signal for which, instead of using block transforms, we use lapped orthogonal transforms for sparse representation. 2) Recovery of a sparse, time-varying signal that follows a linear dynamic model. For both the systems, we iteratively process measurements over a sliding interval and estimate sparse coefficients by solving a weighted L1-norm minimization program. Instead of solving a new L1 program from scratch at every iteration, we use an available signal estimate as a starting point in a homotopy formulation. Starting with a warm-start vector, our homotopy algorithm updates the solution in a small number of computationally inexpensive steps as the system changes. The homotopy algorithm presented in this paper is highly versatile as it can update the solution for the L1 problem in a number of dynamical settings. We demonstrate with numerical experiments that our proposed streaming recovery framework outperforms the methods that represent and reconstruct a signal as independent, disjoint blocks, in terms of quality of reconstruction, and that our proposed homotopy-based updating scheme outperforms current state-of-the-art solvers in terms of the computation time and complexity.

We propose an approximation of the Possible Worlds Semantics (PWS) for action planning. A corresponding planning system is implemented by a transformation of the action specification to an Answer-Set Program. A novelty is support for postdiction wrt. (a) the plan existence problem in our framework can be solved in NP, as compared to $\Sigma_2^P$ for non-approximated PWS of Baral(2000); and (b) the planner generates optimal plans wrt. a minimal number of actions in $\Delta_2^P$. We demo the planning system with standard problems, and illustrate its integration in a larger software framework for robot control in a smart home.

The random drift particle swarm optimization (RDPSO) algorithm, inspired by the free electron model in metal conductors placed in an external electric field, is presented, systematically analyzed and empirically studied in this paper. The free electron model considers that electrons have both a thermal and a drift motion in a conductor that is placed in an external electric field. The motivation of the RDPSO algorithm is described first, and the velocity equation of the particle is designed by simulating the thermal motion as well as the drift motion of the electrons, both of which lead the electrons to a location with minimum potential energy in the external electric field. Then, a comprehensive analysis of the algorithm is made, in order to provide a deep insight into how the RDPSO algorithm works. It involves a theoretical analysis and the simulation of the stochastic dynamical behavior of a single particle in the RDPSO algorithm. The search behavior of the algorithm itself is also investigated in detail, by analyzing the interaction between the particles. Some variants of the RDPSO algorithm are proposed by incorporating different random velocity components with different neighborhood topologies. Finally, empirical studies on the RDPSO algorithm are performed by using a set of benchmark functions from the CEC2005 benchmark suite. Based on the theoretical analysis of the particle's behavior, two methods of controlling the algorithmic parameters are employed, followed by an experimental analysis on how to select the parameter values, in order to obtain a good overall performance of the RDPSO algorithm and its variants in real-world applications. A further performance comparison between the RDPSO algorithms and other variants of PSO is made to prove the efficiency of the RDPSO algorithms.

The problem of adaptive noisy clustering is investigated. Given a set of noisy observations $Z_i=X_i+\epsilon_i$, $i=1,...,n$, the goal is to design clusters associated with the law of $X_i$'s, with unknown density $f$ with respect to the Lebesgue measure. Since we observe a corrupted sample, a direct approach as the popular {\it $k$-means} is not suitable in this case. In this paper, we propose a noisy $k$-means minimization, which is based on the $k$-means loss function and a deconvolution estimator of the density $f$. In particular, this approach suffers from the dependence on a bandwidth involved in the deconvolution kernel. Fast rates of convergence for the excess risk are proposed for a particular choice of the bandwidth, which depends on the smoothness of the density $f$. Then, we turn out into the main issue of the paper: the data-driven choice of the bandwidth. We state an adaptive upper bound for a new selection rule, called ERC (Empirical Risk Comparison). This selection rule is based on the Lepski's principle, where empirical risks associated with different bandwidths are compared. Finally, we illustrate that this adaptive rule can be used in many statistical problems of $M$-estimation where the empirical risk depends on a nuisance parameter.

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on the minimization of the empirical risk. We focus on problems without strong convexity, for which all previously known algorithms achieve a convergence rate for function values of O(1/n^{1/2}). We consider and analyze two algorithms that achieve a rate of O(1/n) for classical supervised learning problems. For least-squares regression, we show that averaged stochastic gradient descent with constant step-size achieves the desired rate. For logistic regression, this is achieved by a simple novel stochastic gradient algorithm that (a) constructs successive local quadratic approximations of the loss functions, while (b) preserving the same running time complexity as stochastic gradient descent. For these algorithms, we provide a non-asymptotic analysis of the generalization error (in expectation, and also in high probability for least-squares), and run extensive experiments on standard machine learning benchmarks showing that they often outperform existing approaches.