This paper introduces a family of local feature aggregation functions and a novel method to estimate their parameters, such that they generate optimal representations for classification (or any task that can be expressed as a cost function minimization problem). To achieve that, we compose the local feature aggregation…
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “local cost functions”
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
A new method reduces communication costs in decentralized optimization.
problem Decentralized optimization with non-convex cost functions.
method LU-GT method with local updates.
result LU-GT achieves the same communication complexity as Federated Learning and maintains solution quality.
In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node up…
Paper optimizes multi-fidelity function with fast learning rates.
problem Optimizing a locally smooth function with limited budget and varying fidelity approximations.
method Kometo algorithm that achieves simple regret rates without knowing function smoothness or fidelity assumptions.
result Kometo algorithm outperforms previous methods empirically.
In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiase…
Derives inequality for optimal transport on manifolds.
problem Optimal transport theory on manifolds.
method Five gradients inequality for cost functions on Lie groups and Riemannian manifolds.
result Derives inequality for optimal transport on specific manifolds.
CAGES: Cost-Aware Gradient Entropy Search for Efficient Local Multi-Fidelity Bayesian Optimizationcs.LG
CAGES optimizes expensive RL problems by efficiently learning gradients from multiple sources.
problem Optimizing expensive-to-evaluate functions in high-dimensional spaces.
method Cost-Aware Gradient Entropy Search (CAGES) for multi-fidelity Bayesian optimization.
result Significant performance improvements on synthetic and RL benchmark problems.
Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost…
We present a novel optimization method, named the Combined Optimization Method (COM), for the joint optimization of two or more cost functions. Unlike the conventional joint optimization schemes, which try to find minima in a weighted sum of cost functions, the COM explores search space for common minima shared by all …
This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…
New findings show different cost functions yield equivalent curvature bounds.
problem Establishing equivalence of curvature bounds under various transport costs.
method Needle decomposition and localization technique for optimal transport.
result All conditions are equivalent for .
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with …
Finite-Time Convergence of Continuous-Time Optimization Algorithms via Differential Inclusionsmath.OC
In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based differential inequality for differential inclusions, which leads to finite-time …
The paper constructs upper bounds for cost minimization in shallow neural networks.
problem Cost minimization in underparametrized shallow ReLU networks.
method Explicit construction of upper bounds based on the geometric structure of classification data.
result An upper bound on the minimum of the cost function of order , with exact degenerate local minimum in the special case .
New algorithm reduces misclassification costs in neural networks.
problem Reduces costs of misclassified instances in neural networks.
method Adaptive Cost-Sensitive Learning (AdaCSL) adjusts loss function to bridge class distribution mismatches.
result Deep neural networks with AdaCSL outperform other methods on cost-sensitive binary classification tasks.
Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Eucli…
This paper accelerates distributed convex optimization by mitigating ill-conditioning issues.
problem Distributed convex optimization with ill-conditioned aggregate cost functions.
method Iterative pre-conditioning technique to improve convergence rate and stability.
result The proposed algorithm converges linearly with improved convergence rate and superlinearly under certain conditions.
The paper constructs minimizers for deep learning networks and analyzes their geometric structure.
problem Underparametrized deep learning networks and their minimizers.
method Direct construction of minimizers without gradient descent, considering specific settings.
result Explicit family of minimizers for the global minimum and a set of degenerate local minima.
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent Lévy measure. We present a pricing method for Bermudan options based on an analytical approximatio…
We regard the real symplectic group as a constraint submanifold of the real matrices endowed with the Euclidean (Frobenius) metric, respectively as a submanifold of the general linear group endowed with the (left) invariant metric. For…
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror des…
Paper proposes a pre-conditioning method to speed up gradient descent in multi-agent optimization.
problem Speed up convergence of gradient descent in multi-agent optimization problems.
method Iterative pre-conditioning approach to mitigate the effect of problem conditioning.
result Significant improvement in convergence speed of gradient descent method.
Efficient local planning with linear approximations for agents with limited simulator access.
problem Planning with limited simulator access in reinforcement learning.
method Confident Monte Carlo Least Square Policy Iteration (Confident MC-LSPI) and Politex (Confident MC-Politex) algorithms.
result The algorithms can learn the optimal policy with local simulator access, even for linear Q-functions.
Evolution of the distribution of wealth in an economic environment driven by local Nash equilibriaq-fin.GN
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general assumptions on the cost function. This evolution drives the dynamic of the agents i…
Enhances Random Forest for imbalanced functional data classification.
problem Challenges in classifying imbalanced functional data.
method Functional Random Forest with Adaptive Cost-Sensitive Splitting (FRF-ACS).
result Significantly improves minority class recall and predictive performance.
Families of costs with zero and nonnegative MTW tensor in optimal transport and the c-divergencesmath.AP
Study optimal transport costs with zero MTW tensor, finding new families of costs and divergence functions.
problem Characterize optimal transport costs with zero MTW tensor.
method Optimal transport theory, information geometry, solving nonlinear ODEs.
result Found new families of costs and divergence functions.
We identify a condition for regularity of optimal transport maps that requires only three derivatives of the cost function, for measures given by densities that are only bounded above and below. This new condition is equivalent to the weak Ma-Trudinger-Wang condition when the cost is . Moreover, we only require (n…
The paper considers a class of multi-agent Markov decision processes (MDPs), in which the network agents respond differently (as manifested by the instantaneous one-stage random costs) to a global controlled state and the control actions of a remote controller. The paper investigates a distributed reinforcement learnin…
Optimal algorithms for non-linear ridge bandits reduce burn-in cost.
problem Non-linear models introduce a burn-in period with fixed cost.
method Two-stage algorithm: find initial action, then treat locally linear.
result Two-stage algorithm is statistically optimal.
BO limits search to lower dimensions with LGPR, improving efficiency and accuracy.
problem High computational costs in BO for high-dimensional optimization.
method Limits search region to lower dimensions and uses LGPR for local Gaussian process regression.
result Search efficiencies improved by about 69% and 40% for Ackley and Rosenbrock functions.
Federated learning (FL) is a distributed learning approach where a set of end-user devices participate in the learning process by acting on their isolated local data sets. Here, we process local data sets of users where worst-case optimization theory is used to reformulate the FL problem where the impact of local data …
New kernels capture both local and non-local interactions efficiently.
problem Designing kernels that capture both local and non-local interactions while remaining computationally tractable.
method Spectral truncation kernels based on -algebra.
result Spectral truncation kernels induce interactions across the data function domain and reduce computational cost.
A new method reduces the complexity of decentralized optimization.
problem Decentralized stochastic non-convex optimization over a network.
method GT-HSGD, a hybrid variance-reduced method.
result Achieves an oracle complexity of O(n^(-1)ε^(-3)) for small ε.
Taylor Learningstat.ML
New learning algorithm for real analytic functions without gradient descent.
problem Learning real analytic functions without gradient descent.
method Taylor approximation and sampling data distribution.
result Nonuniform learning result for real analytic functions.
FedElasticNet reduces communication costs and handles client drift in FL.
problem Expensive communication costs and client drift issues in federated learning.
method Leverages elastic net regularizers to sparsify local updates and limit client drift.
result FedElasticNet effectively resolves communication cost and client drift problems.
It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only…
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these co…
Traditional plane-based clustering methods measure the cost of within-cluster and between-cluster by quadratic, linear or some other unbounded functions, which may amplify the impact of cost. This letter introduces a ramp cost function into the plane-based clustering to propose a new clustering method, called ramp-base…
A distributed semismooth Newton based augmented Lagrangian method for distributed optimizationmath.OC
A new method solves distributed optimization problems over networks.
problem Solving optimization problems over networks with local cost functions and limited communication.
method Distributed semismooth Newton based augmented Lagrangian method.
result The method efficiently solves distributed optimization problems over networks.
Almost all local minima in neural networks are strongly convex.
problem The prevalence of strongly convex neighborhoods around local minima in neural network optimization landscapes.
method Rigorous analysis of shallow neural networks with analytic activation functions, dividing parameter space into efficient and redundant domains.
result For shallow neural networks on the efficient domain, almost all local minima are strongly convex.
Study absolute continuity of Wasserstein barycenters on manifolds with singular cost functions.
problem Absolute continuity of Wasserstein barycenters on manifolds with singular cost functions.
method Approximation framework to handle singularity, geometrically transparent.
result Precise analytic condition on cost profile for necessary assumptions.
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configu…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality and small sample size . More specifically, we consider a function defined by local sparse models, one at each data point. We introduce sample-wis…
Optimal liquidation model reduces trading costs in OTC markets.
problem Minimizing trading costs in Over-The-Counter markets.
method Developed an optimal portfolio liquidation model in Locally Linear Order Book framework.
result Optimal liquidation time is proportional to the square root of the traded volume.
Update rules for learning in dynamic time warping spaces are based on optimal warping paths between parameter and input time series. In general, optimal warping paths are not unique resulting in adverse effects in theory and practice. Under the assumption of squared error local costs, we show that no two warping paths …
Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functionsmath.OC
Adaptive replication improves stochastic function optimization.
problem Challenges in accurately estimating functions with high variance.
method Trust-region-based Bayesian optimization with adaptive replication.
result Adaptive replication substantially improves solution accuracy and efficiency.
New method optimizes hyperparameters for non-smooth problems efficiently.
problem Efficiently tuning hyperparameters for non-smooth cost functions.
method Combines hyperparameter search with proximal gradient updates.
result Method converges to local optimum of LOO validation error.