Daniel Keren

Daniel Keren

Cheating in chess, by using advice from powerful software, has become a major problem, reaching the highest levels. As opposed to the large majority of previous work, which concerned {\em detection} of cheating, here we try to evaluate the possible gain in performance, obtained by cheating a limited number of times during a game. Algorithms are developed and tested on a commonly used chess engine (i.e software).\footnote{Needless to say, the goal of this work is not to assist cheaters, but to measure the effectiveness of cheating -- which is crucial as part of the effort to contain and detect it.}

Daniel Keren, Margarita Osadchy, Roi Poranne

Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main advantage of this transormation is that SDP is a convex problem for which efficient solvers are readily available. However, while considerable progress has been made in recent years, the standard approaches for solving SDPs are still known to scale poorly. Our goal is to devise an approach that can handle larger, more complex problems than is currently possible. The challenge indeed lies in how SDPs are commonly solved. State-Of-The-Art approaches rely on the interior point method, which requires the factorization of large matrices. We instead propose an approach inspired by polynomial neural networks, which exhibit excellent performance when optimized using techniques from the deep learning toolbox. In a somewhat counter-intuitive manner, we replace the convex SDP formulation with a non-convex, unconstrained, and \emph{over parameterized} formulation, and solve it using a first order optimization method. It turns out that this approach can handle very large problems, with polynomials having over four million coefficients, well beyond the range of current SDP-based approaches. Furthermore, we highlight theoretical and practical results supporting the experimental success of our approach in avoiding spurious local minima, which makes it amenable to simple and fast solutions based on gradient descent. In all the experiments, our approach had always converged to a correct global minimum, on general (non-sparse) polynomials, with running time only slightly higher than linear in the number of polynomial coefficients, compared to higher than quadratic in the number of coefficients for SDP-based methods.

Michael Kamp, Mario Boley, Michael Mock et al.

We consider distributed online learning protocols that control the exchange of information between local learners in a round-based learning scenario. The learning performance of such a protocol is intuitively optimal if approximately the same loss is incurred as in a hypothetical serial setting. If a protocol accomplishes this, it is inherently impossible to achieve a strong communication bound at the same time. In the worst case, every input is essential for the learning performance, even for the serial setting, and thus needs to be exchanged between the local learners. However, it is reasonable to demand a bound that scales well with the hardness of the serialized prediction problem, as measured by the loss received by a serial online learning algorithm. We provide formal criteria based on this intuition and show that they hold for a simplified version of a previously published protocol.