A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Research shows minimal communication limits adaptive function estimation rates.
problem Adaptive estimation of a smooth function under minimal communication constraints.
method Investigates the L∞-risk and L2-risk under different numbers of servers.
result For L∞-risk, optimal rates cannot be achieved under minimal communication. For L2-risk, adaptivity is possible but depends on server number and sample size.
This research improves neural network performance with adaptive activation functions in sparse data settings.
problem Limited data availability in scientific and engineering problems.
method Investigation of two types of adaptive activation functions with individual trainable parameters.
result Adaptive activation functions, especially with individual trainable parameters, enhance prediction accuracy and confidence in sparse data settings.
The most widely used activation functions in current deep feed-forward neural networks are rectified linear units (ReLU), and many alternatives have been successfully applied, as well. However, none of the alternatives have managed to consistently outperform the rest and there is no unified theory connecting properties…
To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms have been successfully developed to minimize the adaptive regret. However, existi…
A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…
Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.
problem Maximizing submodular functions subject to constraints in linear time.
method Developed linear-time algorithms for two submodular maximization problems: adaptive and fully adaptive.
result Achieved (1−1/e−ε) approximation ratio for adaptive submodular maximization and $ rac{1-1/e-ε}{4-2/e-2ε}$ for fully adaptive submodular maximization.
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable function…
We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each lay…
Many neural network architectures rely on the choice of the activation function for each hidden layer. Given the activation function, the neural network is trained over the bias and the weight parameters. The bias catches the center of the activation, and the weights capture the scale. Here we propose to train the netw…
We study a non-parametric multi-armed bandit problem with stochastic covariates, where a key complexity driver is the smoothness of payoff functions with respect to covariates. Previous studies have focused on deriving minimax-optimal algorithms in cases where it is a priori known how smooth the payoff functions are. I…
Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its key ingredient is an acquisition function that changes as a function of previou…
In this paper, we consider adaptive decision-making problems for stochastic state estimation with partial observations. First, we introduce the concept of weak adaptive submodularity, a generalization of adaptive submodularity, which has found great success in solving challenging adaptive state estimation problems. The…
In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{ö}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli an…
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels us…
In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the L∞ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of complexity and use it to prove that, for each convex function f⋆, our …
We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time. Different from previous works that only utilize the convexity condition, this pa…