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Lazy caterer jigsaw puzzles: Models, properties, and a mechanical system-based solver

arXiv.org Artificial Intelligence

Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered fragments, is fundamental to numerous applications, and yet most of the literature has focused thus far on less realistic puzzles whose pieces are identical squares. Here we formalize a new type of jigsaw puzzle where the pieces are general convex polygons generated by cutting through a global polygonal shape with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer's sequence. We analyze the theoretical properties of such puzzles, including the inherent challenges in solving them once pieces are contaminated with geometrical noise. To cope with such difficulties and obtain tractable solutions, we abstract the problem as a multi-body spring-mass dynamical system endowed with hierarchical loop constraints and a layered reconstruction process. We define evaluation metrics and present experimental results to indicate that such puzzles are solvable completely automatically.


Excursion Search for Constrained Bayesian Optimization under a Limited Budget of Failures

arXiv.org Machine Learning

When learning to ride a bike, a child falls down a number of times before achieving the first success. As falling down usually has only mild consequences, it can be seen as a tolerable failure in exchange for a faster learning process, as it provides rich information about an undesired behavior. In the context of Bayesian optimization under unknown constraints (BOC), typical strategies for safe learning explore conservatively and avoid failures by all means. On the other side of the spectrum, non conservative BOC algorithms that allow failing may fail an unbounded number of times before reaching the optimum. In this work, we propose a novel decision maker grounded in control theory that controls the amount of risk we allow in the search as a function of a given budget of failures. Empirical validation shows that our algorithm uses the failures budget more efficiently in a variety of optimization experiments, and generally achieves lower regret, than state-of-the-art methods. In addition, we propose an original algorithm for unconstrained Bayesian optimization inspired by the notion of excursion sets in stochastic processes, upon which the failures-aware algorithm is built.


From Chess and Atari to StarCraft and Beyond: How Game AI is Driving the World of AI

arXiv.org Artificial Intelligence

This paper reviews the field of Game AI, which not only deals with creating agents that can play a certain game, but also with areas as diverse as creating game content automatically, game analytics, or player modelling. While Game AI was for a long time not very well recognized by the larger scientific community, it has established itself as a research area for developing and testing the most advanced forms of AI algorithms and articles covering advances in mastering video games such as StarCraft 2 and Quake III appear in the most prestigious journals. Because of the growth of the field, a single review cannot cover it completely. Therefore, we put a focus on important recent developments, including that advances in Game AI are starting to be extended to areas outside of games, such as robotics or the synthesis of chemicals. In this article, we review the algorithms and methods that have paved the way for these breakthroughs, report on the other important areas of Game AI research, and also point out exciting directions for the future of Game AI.


Efficient Learning of Distributed Linear-Quadratic Controllers

arXiv.org Machine Learning

In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed controllers can be learned with sub-linear sample complexity and computed with near-linear time complexity, both measured with respect to the dimension of the system. In particular, we provide sharp end-to-end guarantees on the stability and the performance of the designed distributed controller and prove that for sparse systems, the number of samples needed to guarantee robust and near optimal performance of the designed controller can be significantly smaller than the dimension of the system. Finally, we show that the proposed optimization problem can be solved to global optimality with near-linear time complexity by iteratively solving a series of small quadratic programs.


A Review of Tracking, Prediction and Decision Making Methods for Autonomous Driving

arXiv.org Machine Learning

The models are updated using a CNN, which ensures robustness to noise, scaling and minor variations of the targets' appearance. As with many other related approaches, an online implementation offloads most of the processing to an external server leaving the embedded device from the vehicle to carry out only minor and frequently-needed tasks. Since quick reactions of the system are crucial for proper and safe vehicle operation, performance and a rapid response of the underlying software is essential, which is why the online approach is popular in this field. Also in the context of ensuring robustness and stability, some authors apply fusion techniques to information extracted from CNN layers. It has been previously mentioned that important correlations can be drawn from deep and shallow layers which can be exploited together for identifying robust features in the data.


Factored Contextual Policy Search with Bayesian Optimization

arXiv.org Artificial Intelligence

Scarce data is a major challenge to scaling robot learning to truly complex tasks, as we need to generalize locally learned policies over different task contexts. Contextual policy search offers data-efficient learning and generalization by explicitly conditioning the policy on a parametric context space. In this paper, we further structure the contextual policy representation. We propose to factor contexts into two components: target contexts that describe the task objectives, e.g. target position for throwing a ball; and environment contexts that characterize the environment, e.g. initial position or mass of the ball. Our key observation is that experience can be directly generalized over target contexts. We show that this can be easily exploited in contextual policy search algorithms. In particular, we apply factorization to a Bayesian optimization approach to contextual policy search both in sampling-based and active learning settings. Our simulation results show faster learning and better generalization in various robotic domains. See our supplementary video: https://youtu.be/MNTbBAOufDY.