arXiv research

New algorithms improve on consistency and robustness in convex function chasing with black-box advice.

Funds inflate their returns due to price pressure, leading to wealth reallocation and market crashes.

We study online optimization in a setting where an online learner seeks to optimize a per-round hitting cost, which may be non-convex, while incurring a movement cost when changing actions between rounds. We ask: \textit{under what general conditions is it possible for an online learner to leverage predictions of futur…

We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei and Luo, 2018) is in fact not improvable for adaptive adversary. Despite this neg…

We have studied statistical characteristics of five share price time series. For each stock price, we estimated a best fit quantitative model for the monthly closing price as based on the decomposition into two defining consumer price indices selected from a large set of CPIs. It was found that there are two pairs of s…

For a smooth family of exact forms on a smooth manifold, an algorithm for computing a primitive family smoothly dependent on parameters is given. The algorithm is presented in the context of a diagram chasing argument in the Čech-de Rham complex. In addition, explicit formulas for such primitive family are presented.

Optimizes non-linear outcomes from summed contributions.

We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally differentially private protocols as straightforward corollaries of results from com…

A blockchain replaces central counterparties with time-consuming consensus protocols to record the transfer of ownership. This settlement latency slows cross-exchange trading, exposing arbitrageurs to price risk. Off-chain settlement, instead, exposes arbitrageurs to costly default risk. We show with Bitcoin network an…

In distributed function computation, each node has an initial value and the goal is to compute a function of these values in a distributed manner. In this paper, we propose a novel token-based approach to compute a wide class of target functions to which we refer as "Token-based function Computation with Memory" (TCM) …

Randomness is crucial for stability in learning and statistics, especially for differential privacy.

This paper proposes a method to train energy-based models using variational auto-encoders for efficient sampling.

Reservoir Computing (RC) provides an efficient way for designing dynamical recurrent neural models. While training is restricted to a simple output component, the recurrent connections are left untrained after initialization, subject to stability constraints specified by the Echo State Property (ESP). Literature condit…

Existing supervised approaches didn't make use of the low-level features which are actually effective to this task. And another deficiency is that they didn't consider the relation between pixels, which means effective features are not extracted. In this paper, we proposed a novel convolutional neural network which mak…

Researchers adaptively analyze market regimes to reveal investor behavior shifts.

Oeljeklaus-Toma (OT) manifolds are certain compact complex manifolds built from number fields. Conversely, we show that the fundamental group often pins down the number field uniquely. We relate the first homology to some interesting ideal. OT manifolds are never Kähler, but carry an LCK metric (locally conformally Käh…

The paper studies quasi-$X$-convex functions and their applications in optimization.

The retinal vascular condition is a reliable biomarker of several ophthalmologic and cardiovascular diseases, so automatic vessel segmentation may be crucial to diagnose and monitor them. In this paper, we propose a novel method that combines the multiscale analysis provided by the Stationary Wavelet Transform with a m…

As a generalization of geodesic function, in the present paper, we introduce the notion of geodesic $\varphi$-convex function and deduce some basic properties of $\varphi$-convex function and geodesic $\varphi$-convex function. We also introduce the concept of geodesic $\varphi$-convex set and $\varphi$-epigraph and in…

New geometric proof of convex function differentiability and approximation.

The study of infinite groups through their finite quotients in geometry.

The paper shows that g-convex functions on manifolds are sparse.

Let $U\subseteq\mathbb{R}^d$ be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function $f:U\to\mathbb{R}$ can be approximated by real analytic convex functions, uniformly on all of $U$. We also show that $C^0$-fine approximation of convex functions by smooth (or real analytic) conv…

We show that $C^0$-fine approximation of convex functions by smooth (or real analytic) convex functions on $\R^d$ is possible in general if and only if $d=1$. Nevertheless, for $d\geq 2$ we give a characterization of the class of convex functions on $\R^d$ which can be approximated by real analytic (or just smoother) c…

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{μν})$ or an initial data set $(Σ, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how…

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{μν})$ or an initial data set $(Σ, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how…

Let $U\subseteq\mathbb{R}^{n}$ be open and convex. We show that every (not necessarily Lipschitz or strongly) convex function $f:U\to\mathbb{R}$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded …

The paper connects convex functions to p-subharmonic functions and proves their equivalence.

This paper studies quasar-convex functions to improve optimization methods.

Least Squares Estimators are suboptimal for 5D convex functions.

The study links Ricci curvature and convexity in complex tori.

Extends DCP framework to Hadamard manifolds for geodesically convex functions.

New neural network approximates convex option prices.

First order methods can take extremely long to find global minima of non-convex functions.

Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation techniques to find a convex surrogate for the problem. Unfortunately, convex relaxat…

Study on convex ordering in stochastic control for swing contracts, proving value function convexity.

Optimally shows the distance between perturbed convex functions and their Γ-regularizations.

Classifies geodetically convex sets and functions on Heisenberg group.

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…

Study beta function for convex billiard maps, linking spectral invariants.

Convex functions and bodies can be approximated by smoother convex functions.

New method for optimization on Hadamard manifolds with curvature-independent guarantees.

AGGLIO optimizes non-convex functions with local convexity guarantees.

Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the related variational problems and optimization problems. Random convex analysis is …

This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.

In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this algorithm is a sequence of pairs of convex functions that converge uniformly to a p…

Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, sub-modular functions or supermodular functions separately while …