arXiv research

A new method extracts features from time series data using iterated sums and improves classification accuracy.

Gradient methods converge exponentially in concave network games.

Mutation improves FTRL convergence in zero-sum games.

Optimizes convergence rate of stochastic proximal algorithms for composite convex problems.

Contact connected sums do not increase support genus.

New algorithms converge faster to Nash equilibrium in zero-sum games with bandit feedback.

Accelerates optimization in asynchronous systems with sparse updates.

We study the conditions under which one is able to efficiently apply variance-reduction and acceleration schemes on finite sum optimization problems. First, we show that, perhaps surprisingly, the finite sum structure by itself, is not sufficient for obtaining a complexity bound of $\tilde{\cO}((n+L/μ)\ln(1/ε))$ for $L…

New method solves root-finding problems with faster convergence.

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of the state. In this work, we compute the solution of the two-player zero-sum game…

New algorithm finds near-optimal policies efficiently in zero-sum games.

New method reduces complexity of minimizing convex finite sums without needing individual function indices.

Efficient reinforcement learning for simultaneous-move zero-sum games using optimistic value iteration.

We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed. For quadratic objectives, we prove improved iteration complexity over state-of-…

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of the terms in the sum. These methods can make great progress initially, but often…

Unified framework for stability and generalization of Push-Sum in decentralized learning over directed graphs.

This paper presents a lower bound for optimizing a finite sum of $n$ functions, where each function is $L$-smooth and the sum is $μ$-strongly convex. We show that no algorithm can reach an error $ε$ in minimizing all functions from this class in fewer than $Ω(n + \sqrt{n(κ-1)}\log(1/ε))$ iterations, where $κ=L/μ$ is a …

The paper approximates financial derivatives using neural networks and iterated integrals.

We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed to contain multiple components such as (i) linear and nonlinear components, (ii)…

We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of constraints compared to popular MIP models based on cycle elimination constraint…

Let M denote the total space of a Lefschetz fibration, obtained by blowing up a Lefschetz pencil on an algebraic surface. We consider the n-fold fibre sum M(n), generalizing the construction of the elliptic surfaces E(n). For a Lefschetz pencil on a simply-connected minimal surface of general type we partially calculat…

Sharp knots and iterated cables lead to ribbon knots or failure of slice-ribbon conjecture.

OMWU shows last iterate convergence in convex-concave games.

Convex message passing algorithms converge to a fixed point.

We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also construct a family of special unitary quasitoric manifolds which contains polynomial gen…

The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both funct…

We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants for covering links is a cobordism invariant of a link, and that this invariant can distinguish some links for which the ordinary Milnor invaria…

New algorithms solve non-convex optimization problems efficiently.

Paper uses SC to estimate hidden interference for WSRM.

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order non-convex optimization remain to be full gradient descent that converges in $O(1/\varep…

New method for inferring time series graph from sparse-group log-sum penalty.

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG me…

Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing regularizer. In this paper, motivated by the success of extrapolation techniques in accele…

The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding: (1) Hausdorff distance, and (2) a sum of total curvature and derivative. High degree Bezier curves are often used as …

Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely on both gradients and Hessians. In principle, second-order methods can require …

Policy gradient method proves convergence in imperfect-information games.

This paper studies a specific blow-up algorithm for sop polynomials and their RLCT.

Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. We study two forms of sketching that…

Study on convergence of Langevin dynamics for zero-sum games in probability distributions.

We study the performance of a family of randomized parallel coordinate descent methods for minimizing the sum of a nonsmooth and separable convex functions. The problem class includes as a special case L1-regularized L1 regression and the minimization of the exponential loss ("AdaBoost problem"). We assume the input da…

Investment strategy optimizes risk using a specific risk measure.

Following the lines of a celebrated result by R. Bott (Comm. Pure Appl. Math. 9, 1956) we study the Morse index of the iterated of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic $γ$, w…

DESTRESS optimizes decentralized nonconvex optimization with optimal IFO complexity and efficient communication.

In many distributed learning problems, the heterogeneous loading of computing machines may harm the overall performance of synchronous strategies. In this paper, we propose an effective asynchronous distributed framework for the minimization of a sum of smooth functions, where each machine performs iterations in parall…

We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In particular, we can easily construct complete metrics of constant positive scalar cu…

Entropy-based decoding improves DLM sampling efficiency.

New bounds for SGD show improved performance in various settings.

Quantum algorithms improve calculation of parameter sensitivities in financial derivatives.