In this paper, we consider a temporal logic planning problem in which the objective is to find an infinite trajectory that satisfies an optimal selection from a set of soft specifications expressed in linear temporal logic (LTL) while nevertheless satisfying a hard specification expressed in LTL. Our previous work considered a similar problem in which linear dynamic logic for finite traces (LDLf), rather than LTL, was used to express the soft constraints. In that work, LDLf was used to impose constraints on finite prefixes of the infinite trajectory. By using LTL, one is able not only to impose constraints on the finite prefixes of the trajectory, but also to set `soft' goals across the entirety of the infinite trajectory. Our algorithm first constructs a product automaton, on which the planning problem is reduced to computing a lasso with minimum cost. Among all such lassos, it is desirable to compute a shortest one. Though we prove that computing such a shortest lasso is computationally hard, we also introduce an efficient greedy approach to synthesize short lassos nonetheless. We present two case studies describing an implementation of this approach, and report results of our experiment comparing our greedy algorithm with an optimal baseline.

The last decades have brought enormous technological progress and innovation. Two main factors that are undoubtedly key to this development are (i) hardware advancement and (ii) algorithm advancement. Moore's Law, the prediction made by Gordon Moore in 1965 [55], that the number of components per integrated circuit doubles every year, has shown to be astonishingly accurate for several decades. Given such an exponential improvement on the hardware side, one is tempted to overlook the progress made on the algorithmic side. This paper aims to compare the impact of hardware advancement and algorithm advancement based on a genuine problem, the propositional satisfiability problem (SAT).

Multitask learning and related areas such as multi-source domain adaptation address modern settings where datasets from $N$ related distributions $\{P_t\}$ are to be combined towards improving performance on any single such distribution ${\cal D}$. A perplexing fact remains in the evolving theory on the subject: while we would hope for performance bounds that account for the contribution from multiple tasks, the vast majority of analyses result in bounds that improve at best in the number $n$ of samples per task, but most often do not improve in $N$. As such, it might seem at first that the distributional settings or aggregation procedures considered in such analyses might be somehow unfavorable; however, as we show, the picture happens to be more nuanced, with interestingly hard regimes that might appear otherwise favorable. In particular, we consider a seemingly favorable classification scenario where all tasks $P_t$ share a common optimal classifier $h^*,$ and which can be shown to admit a broad range of regimes with improved oracle rates in terms of $N$ and $n$. Some of our main results are as follows: $\bullet$ We show that, even though such regimes admit minimax rates accounting for both $n$ and $N$, no adaptive algorithm exists; that is, without access to distributional information, no algorithm can guarantee rates that improve with large $N$ for $n$ fixed. $\bullet$ With a bit of additional information, namely, a ranking of tasks $\{P_t\}$ according to their distance to a target ${\cal D}$, a simple rank-based procedure can achieve near optimal aggregations of tasks' datasets, despite a search space exponential in $N$. Interestingly, the optimal aggregation might exclude certain tasks, even though they all share the same $h^*$.

We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations (a.k.a. blind deconvolution under a subspace model). Despite the wide applicability, the theoretical understanding about these two paradigms remains largely inadequate in the presence of noise. The current paper makes two contributions by demonstrating that: (1) convex relaxation achieves minimax-optimal statistical accuracy vis-\`a-vis random noise, and (2) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations. Both results improve upon the state-of-the-art results by some factors that scale polynomially in the problem dimension.

In this paper, several techniques for learning game state evaluation functions by reinforcement are proposed. The first is a generalization of tree bootstrapping (tree learning): it is adapted to the context of reinforcement learning without knowledge based on non-linear functions. With this technique, no information is lost during the reinforcement learning process. The second is a modification of minimax with unbounded depth extending the best sequences of actions to the terminal states. This modified search is intended to be used during the learning process. The third is to replace the classic gain of a game (+1 / -1) with a reinforcement heuristic. We study particular reinforcement heuristics such as: quick wins and slow defeats ; scoring ; mobility or presence. The four is another variant of unbounded minimax, which plays the safest action instead of playing the best action. This modified search is intended to be used after the learning process. The five is a new action selection distribution. The conducted experiments suggest that these techniques improve the level of play. Finally, we apply these different techniques to design program-players to the game of Hex (size 11 and 13) surpassing the level of Mohex 2.0 with reinforcement learning from self-play without knowledge. At Hex size 11 (without swap), the program-player reaches the level of Mohex 3HNN.

We consider the classical problem of sequential probability assignment under logarithmic loss while competing against an arbitrary, potentially nonparametric class of experts. We obtain tight bounds on the minimax regret via a new approach that exploits the self-concordance property of the logarithmic loss. We show that for any expert class with (sequential) metric entropy $\mathcal{O}(\gamma^{-p})$ at scale $\gamma$, the minimax regret is $\mathcal{O}(n^{p/(p+1)})$, and that this rate cannot be improved without additional assumptions on the expert class under consideration. As an application of our techniques, we resolve the minimax regret for nonparametric Lipschitz classes of experts.

For state-of-the-art network function virtualization (NFV) systems, it remains a key challenge to conduct effective service chain composition for different network services (NSs) with ultra-low request latencies and minimum network congestion. To this end, existing solutions often require full knowledge of the network state, while ignoring the privacy issues and overlooking the non-cooperative behaviors of users. What is more, they may fall short in the face of unexpected failures such as user unavailability and virtual machine breakdown. In this paper, we formulate the problem of service chain composition in NFV systems with failures as a non-cooperative game. By showing that such a game is a weighted potential game and exploiting the unique problem structure, we propose two effective distributed schemes that guide the service chain compositions of different NSs towards the Nash equilibrium (NE) state with both near-optimal latencies and minimum congestion. Besides, we develop two novel learning-aided schemes as comparisons, which are based on deep reinforcement learning (DRL) and Monte Carlo tree search (MCTS) techniques, respectively. Our theoretical analysis and simulation results demonstrate the effectiveness of our proposed schemes, as well as the adaptivity when faced with failures.

You will learn about variables, conditional execution, repeated execution and how we use functions. Once a student completes this course, they will be ready to take more advanced programming courses. This course covers Python 3. 4. Programming for the Web with JavaScript Course by University of Pennsylvania The basics of how the World Wide Web allows browsers to send and retrieve web content; Web browser internals, the Document Object Model (DOM), and jQuery; How to create dynamic, interactive web pages using JavaScript; Techniques for creating data-driven websites using modern web technologies; Client-side JavaScript libraries and frameworks; Server-side JavaScript application architecture, middleware, HTTP, and RESTful API design 5. Python Basics for Data Science This Python course provides a beginner-friendly introduction to Python for Data Science. Practice through lab exercises, and you'll be ready to create your first Python scripts on your own! 6. Introduction to Computer Science and Programming Using Python An introduction to computer science as a tool to solve real-world analytical problems using Python 3.5.

Automated Machine Learning (AutoML) has emerged to deal with the selection and configuration of algorithms for a given learning task. With the progression of AutoML, several effective methods were introduced, especially for traditional classification and regression problems. Apart from the AutoML success, several issues remain open. One issue, in particular, is the lack of ability of AutoML methods to deal with different types of data. Based on this scenario, this paper approaches AutoML for multi-label classification (MLC) problems. In MLC, each example can be simultaneously associated to several class labels, unlike the standard classification task, where an example is associated to just one class label. In this work, we provide a general comparison of five automated multi-label classification methods -- two evolutionary methods, one Bayesian optimization method, one random search and one greedy search -- on 14 datasets and three designed search spaces. Overall, we observe that the most prominent method is the one based on a canonical grammar-based genetic programming (GGP) search method, namely Auto-MEKA$_{GGP}$. Auto-MEKA$_{GGP}$ presented the best average results in our comparison and was statistically better than all the other methods in different search spaces and evaluated measures, except when compared to the greedy search method.

"The no free lunch theorem calls for prudency when solving ML problems by requiring that you test multiple algorithms and solutions with a clear mind and without prejudice." In a paper titled, 'The Lack of A Priori Distinctions Between Learning Algorithms', that dates back to 1996, David Wolpert explored the following questions: He showed that for any two algorithms, A and B, there are as many scenarios where A will perform worse than B as there are instances where A will outperform B. In short, for all possible problems, average performance of both the algorithms is the same. Although the no free lunch theorem by Wolpert has a more theoretical than practical appeal, there are some implications that should still be taken into account by everyone working with machine learning algorithms. These theorems prove that under a uniform distribution over search problems or learning problems, all algorithms perform equally. Search and learning are key aspects of ML and the NFL theorems have something to deliver here.