In this paper, we present ASPEN+, which extends an existing ASP-based system, ASPEN,for collective entity resolution with two important functionalities: support for local merges and new optimality criteria for preferred solutions. Indeed, ASPEN only supports so-called global merges of entity-referring constants (e.g. author ids), in which all occurrences of matched constants are treated as equivalent and merged accordingly. However, it has been argued that when resolving data values, local merges are often more appropriate, as e.g. some instances of 'J. Lee' may refer to 'Joy Lee', while others should be matched with 'Jake Lee'. In addition to allowing such local merges, ASPEN+ offers new optimality criteria for selecting solutions, such as minimizing rule violations or maximising the number of rules supporting a merge. Our main contributions are thus (1) the formalisation and computational analysis of various notions of optimal solution, and (2) an extensive experimental evaluation on real-world datasets, demonstrating the effect of local merges and the new optimality criteria on both accuracy and runtime.

A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the Karush-Kuhn-Tucker (KKT) conditions, ensuring that its predictions adhere to these optimality criteria. Additionally, since the bounds of the parameter space are known, training batches can be randomly generated without requiring external data. This method trades guaranteed optimality for significant improvements in speed, enabling parallel solving of a class of optimization problems.

The standard approach to Computational Learning Theory is usually formulated within the so-called frequentist approach to Statistics. Within this paradigm one is interested in constructing an estimator, based on a flnite sample, which possesses a small loss (generalization error). While many algorithms have been constructed and analyzed within this context, it is not clear how these approaches relate to standard optimality criteria within the frequentist framework. Two classic optimality criteria within the latter approach are the minimax and admissibility criteria, which charac- terize optimality of estimators in a rigorous and precise fashion [9]. Except in some special cases [12], it is not known whether any of the approaches used within the Learning community lead to optimality in either of the above senses of the word. On the other hand, it is known that under certain regularity conditions, Bayesian estimators lead to either minimax or admissible estimators, and thus to well-deflned optimality in the classical (frequentist) sense. In fact, it can be shown that Bayes estimators are essentially the only estimators which can achieve optimality in the above senses [9]. This optimality feature provides strong motivation for the study of Bayesian approaches in a frequentist setting.

Deploying autonomous robots capable of exploring unknown environments has long been a topic of great relevance to the robotics community. In this work, we take a further step in that direction by presenting an open-source active visual SLAM framework that leverages the accuracy of a state-of-the-art graph-SLAM system and takes advantage of the fast utility computation that exploiting the structure of the underlying pose-graph offers. Through careful estimation of a posteriori weighted pose-graphs, D-optimal decision-making is achieved online with the objective of improving localization and mapping uncertainties as exploration occurs.

Quantifying uncertainty is a key stage in active simultaneous localization and mapping (SLAM), as it allows to identify the most informative actions to execute. However, dealing with full covariance or even Fisher information matrices (FIMs) is computationally heavy and easily becomes intractable for online systems. In this work, we study the paradigm of active graph-SLAM formulated over \textit{SE(n)}, and propose a general relationship between the FIM of the system and the Laplacian matrix of the underlying pose-graph. This link makes possible to use graph connectivity indices as utility functions with optimality guarantees, since they approximate the well-known optimality criteria that stem from optimal design theory. Experimental validation demonstrates that the proposed method leads to equivalent decisions for active SLAM in a fraction of the time.

Autonomous robotic exploration has long attracted the attention of the robotics community and is a topic of high relevance. Deploying such systems in the real world, however, is still far from being a reality. In part, it can be attributed to the fact that most research is directed towards improving existing algorithms and testing novel formulations in simulation environments rather than addressing practical issues of real-world scenarios. This is the case of the fundamental problem of autonomously deciding when exploration has to be terminated or changed (stopping criteria), which has not received any attention recently. In this paper, we discuss the importance of using appropriate stopping criteria and analyse the behaviour of a novel criterion based on the evolution of optimality criteria in active graph-SLAM.

Reinforcement Learning is a theoretical framework for optimizing the behavior of artificial agents. The notion that behavior in the natural world is in some sense optimal is explored by areas such as biomechanics and physical anthropology. These fields propose a variety of candidate optimality criteria as possible formulations of the principles underlying natural motion. Recent developments in computational biomechanics allow us to create articulated models of living creatures with a significant degree of biological realism. I aim to bring these elements together in my research by using Reinforcement Learning to generate optimized behavior in biomechanical simulations. Such a generative approach will allow us to examine critically postulated optimality criteria and investigate hypotheses that cannot be easily studied in the real world.

In reinforcement learning (RL), the goal is to obtain an optimal policy, for which the optimality criterion is fundamentally important. Two major optimality criteria are average and discounted rewards, where the later is typically considered as an approximation to the former. While the discounted reward is more popular, it is problematic to apply in environments that have no natural notion of discounting. This motivates us to revisit a) the progression of optimality criteria in dynamic programming, b) justification for and complication of an artificial discount factor, and c) benefits of directly maximizing the average reward. Our contributions include a thorough examination of the relationship between average and discounted rewards, as well as a discussion of their pros and cons in RL. We emphasize that average-reward RL methods possess the ingredient and mechanism for developing the general discounting-free optimality criterion (Veinott, 1969) in RL.

We study the iteration complexity of stochastic gradient descent (SGD) for minimizing the gradient norm of smooth, possibly nonconvex functions. We provide several results, implying that the classical $\mathcal{O}(\epsilon^{-4})$ upper bound (for making the average gradient norm less than $\epsilon$) cannot be improved upon, unless a combination of additional assumptions is made. Notably, this holds even if we limit ourselves to convex quadratic functions. We also show that for nonconvex functions, the feasibility of minimizing gradients with SGD is surprisingly sensitive to the choice of optimality criteria.

The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency is measured by optimality criteria, including A(verage), D(eterminant), T(race), E(igen), V(ariance) and G-optimality. Except for the T-optimality, exact optimization is NP-hard. We propose a polynomial-time regret minimization framework to achieve a $(1+\varepsilon)$ approximation with only $O(p/\varepsilon^2)$ design points, for all the optimality criteria above. In contrast, to the best of our knowledge, before our work, no polynomial-time algorithm achieves $(1+\varepsilon)$ approximations for D/E/G-optimality, and the best poly-time algorithm achieving $(1+\varepsilon)$-approximation for A/V-optimality requires $k = \Omega(p^2/\varepsilon)$ design points.