Thecomputation ofthecompetitiveequilibrium isknownasthemarketequilibrium computation problem, whose unique solution was shown to exist under a general model of the economics in the seminal work of Arrow and Debreu[3].

Emphasizing issues of computational efficiency, Michael Kearns and Umesh Vazirani introduce a number of central topics in computational learning theory for researchers and students in artificial intelligence, neural networks, theoretical computer science, and statistics. Computational learning theory is a new and rapidly expanding area of research that examines formal models of induction with the goals of discovering the common methods underlying efficient learning algorithms and identifying the computational impediments to learning. Each topic in the book has been chosen to elucidate a general principle, which is explored in a precise formal setting. Intuition has been emphasized in the presentation to make the material accessible to the nontheoretician while still providing precise arguments for the specialist. This balance is the result of new proofs of established theorems, and new presentations of the standard proofs.

We introduce a rich model for multi-objective clustering with lexicographic ordering over objectives and a slack. The slack denotes the allowed multiplicative deviation from the optimal objective value of the higher priority objective to facilitate improvement in lower-priority objectives. We then propose an algorithm called Zeus to solve this class of problems, which is characterized by a makeshift function. The makeshift fine tunes the clusters formed by the processed objectives so as to improve the clustering with respect to the unprocessed objectives, given the slack. We present makeshift for solving three different classes of objectives and analyze their solution guarantees. Finally, we empirically demonstrate the effectiveness of our approach on three applications using real-world data.

Hopes for quantum computing have long been buoyed by the existence of algorithms that would solve some particularly challenging problems with exponentially fewer operations than any known algorithm for conventional computers. Many experts believe, but have been unable to prove, that these problems will resist even the cleverest non-quantum algorithms. Recently, researchers have shown the strongest evidence yet that even if conventional computers were made much more powerful, they probably still could not efficiently solve some problems that a quantum computer could. That such problems exist is a long-standing conjecture about the greater capability of quantum computers. "It was really the first big conjecture in quantum complexity theory," said computer scientist Umesh Vazirani of the University of California, Berkeley, who proposed the conjecture with then-student Ethan Bernstein in the 1993 paper (updated in 1997) that established the field.

In the spring of 2017, Urmila Mahadev found herself in what most graduate students would consider a pretty sweet position. She had just solved a major problem in quantum computation, the study of computers that derive their power from the strange laws of quantum physics. Combined with her earlier papers, Mahadev's new result, on what is called blind computation, made it "clear she was a rising star," said Scott Aaronson, a computer scientist at the University of Texas, Austin. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences. Mahadev, who was 28 at the time, was already in her seventh year of graduate school at the University of California, Berkeley -- long past the stage when most students become impatient to graduate.

Foundations of Machine Learning, by Mehryar Mohri, Afshin Rostamizadeh and Ameet Talwalkar, is a 2012 book on machine learning theory. Understanding Machine Learning: From Theory to Algorithms, by Shai Shalev-Shwartz and Shai Ben-David, is a similar 2014 book that's fairly well-known and targeted a little more introductory than Mohri/Rostamizadeh/Talwalkar, but still has lots of theory in it. Neural Network Learning: Theoretical Foundations, by Martin Anthony and Peter Bartlett, is a 1999 book about ML theory phrased as being about neural networks, but (to my impression not having read it) is mostly about ML theory in general. These three books mostly take the predominant viewpoint of statistical learning theory. There is also an interesting point of view called computational learning theory, inspired more by computer science theory.

Bipartite matching markets pair agents on one side of a market with agents, items, or contracts on the opposing side. Prior work addresses online bipartite matching markets, where agents arrive over time and are dynamically matched to a known set of disposable resources. In this paper, we propose a new model, Online Matching with (offline) Reusable Resources under Known Adversarial Distributions (OM-RR-KAD), in which resources on the offline side are reusable instead of disposable; that is, once matched, resources become available again at some point in the future. We show that our model is tractable by presenting an LP-based adaptive algorithm that achieves an online competitive ratio of 1/2 − ε for any given ε > 0. We also show that no non-adaptive algorithm can achieve a ratio of 1/2 + o(1) based on the same benchmark LP. Through a data-driven analysis on a massive openly-available dataset, we show our model is robust enough to capture the application of taxi dispatching services and ride-sharing systems. We also present heuristics that perform well in practice.

Cheaper and older isn't typically associated with riches and success in the Bay Area tech scene. But that's just what San Jose is offering -- cheaper office rent and older tech workers -- to a rapidly expanding cohort of companies focused on artificial intelligence, the explosive new frontier in tech. "San Francisco has the gamers, we have the grownups," said San Jose Mayor Sam Liccardo. "We've got a very rich pool of talented, skilled workers." Artificial intelligence -- which can be broadly interpreted to include machine learning and the "deep learning" technology that resembles human thought -- is widely seen to be as revolutionary as the internet and mobile phones.

A Canadian firm has courted controversy with its claim to have built a practical quantum computer, a feat thought to be decades away. Now, independent researchers are trying to understand whether it really can tap the strange world of quantum physics. For the modest sum of $15m (£9m), a start-up near Vancouver will sell you a black box the size of a garden shed with its logo emblazoned on the side in white neon. What if I told you the contents of the box were kept colder than the temperature of interstellar space? How about this: The box contains a machine that can solve some of the thorniest mathematical problems and could revolutionise computing.

We address a spatial conservation planning problem in which the planner purchases a budget-constrained set of land parcels in order to maximize the expected spread of a population of an endangered species. Existing techniques based on the sample average approximation scheme and standard integer programming methods have high complexity and limited scalability. We propose a fast combinatorial optimization algorithm using Lagrangian relaxation and primal-dual techniques to solve the problem approximately. The algorithm provides a new way to address a range of conservation planning and scheduling problems. On the Red-cockaded Woodpecker data, our algorithm produces near optimal solutions and runs significantly faster than a standard mixed integer program solver. Compared with a greedy baseline, the solution quality is comparable or better, but our algorithm is 10–30 times faster. On synthetic problems that do not exhibit submodularity, our algorithm significantly outperforms the greedy baseline.