arXiv research

Improved root-finding method for smooth functions.

ThiopheneIV is a new solver for implied volatility with proven monotonicity.

Fast-vollib offers high-performance option pricing and IV computation.

Implicit Q-learning and SARSA adjust step-sizes automatically, improving stability and performance.

Study distortion risk measures for step-weighted distributions.

Dance Dance Revolution (DDR) is a popular rhythm-based video game. Players perform steps on a dance platform in synchronization with music as directed by on-screen step charts. While many step charts are available in standardized packs, players may grow tired of existing charts, or wish to dance to a song for which no …

An adaptive time-stepping controller improves stability and accuracy of ResNets.

The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …

Step decay schedules improve convergence in non-convex optimization.

We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio selection process. At the heart of our algorithm are deep hierarchical compositions of p…

In its simplest form, the traffic flow prediction problem is restricted to predicting a single time-step into the future. Multi-step traffic flow prediction extends this set-up to the case where predicting multiple time-steps into the future based on some finite history is of interest. This problem is significantly mor…

A Levi-Malcev type decomposition for $2$-step solvable Lie algebras with a complex structure

The paper analyzes fixed step-size SA schemes on Riemannian manifolds.

Note on instabilities in super-time-stepping methods for Heston model.

Study on holonomy of Obata connection on specific nilmanifolds.

The study characterizes G₂-structures on 2-step nilpotent Lie groups.

The paper calculates prices for multi-step barrier options under the Black-Scholes model.

We associate a two-step nilpotent Lie algebra to an arbitrary Schreier graph. We then use properties of the Schreier graph to determine necessary and sufficient conditions for this Lie algebra to extend to a three-step nilpotent Lie algebra. As an application, if we start with pairs of non-isomorphic Schreier graphs co…

For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to better performance-complexity trade-offs than their few-step counterparts.

Study geometric step options with jumps, deriving pricing equations and characterizations.

Improved convergence for Polyak steps with momentum in smooth convex optimization.

Chebyshev steps improve convergence in deep-unfolded gradient descent.

Model-based reinforcement learning is an appealing framework for creating agents that learn, plan, and act in sequential environments. Model-based algorithms typically involve learning a transition model that takes a state and an action and outputs the next state---a one-step model. This model can be composed with itse…

One-step diffusion samplers reduce sampling time and computational costs.

The paper analyzes and validates two step size schedules for SGD: exponential and cosine, proving their adaptivity and performance.

Paper adapts ACI for online multi-step time-series forecasting with coverage guarantees.

In this paper, we introduce a method for adapting the step-sizes of temporal difference (TD) learning. The performance of TD methods often depends on well chosen step-sizes, yet few algorithms have been developed for setting the step-size automatically for TD learning. An important limitation of current methods is that…

IMM generates high-quality samples in few steps with stable training.

When environmental interaction is expensive, model-based reinforcement learning offers a solution by planning ahead and avoiding costly mistakes. Model-based agents typically learn a single-step transition model. In this paper, we propose a multi-step model that predicts the outcome of an action sequence with variable …

Proposes a neural network for learning step-size policies for L-BFGS optimization.

Few-step distillation improves T2I models without real images or CFG trade-offs.

Step-DAD improves BED by periodically updating a design policy during experiments.

Multiple-step lookahead policies have demonstrated high empirical competence in Reinforcement Learning, via the use of Monte Carlo Tree Search or Model Predictive Control. In a recent work \cite{efroni2018beyond}, multiple-step greedy policies and their use in vanilla Policy Iteration algorithms were proposed and analy…

The paper introduces a multi-step loss function to improve model-based reinforcement learning.

In this article we prove that the codimension of the abnormal set of the endpoint map for certain classes of Carnot groups of step 2 is at least three. Our result applies to all step 2 Carnot groups of dimension up to 7 and is a generalisation of a previous analogous result for step 2 free nilpotent groups.

New algorithm improves stability of optimization algorithms by adapting step-size.

The paper interprets learned step sizes in deep-unfolded gradient descent.

This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. However, both E and M steps are computationally intractable for high dimensional d…

A two-step nonparametric method estimates financial systemic risk.

Paper tackles catastrophic overfitting in single-step adversarial training.

For some geometries including symplectic and contact structures on an n-dimensional manifold, we introduce a two-step approach to Gromov's h-principle. From formal geometric data, the first step builds a transversely geometric Haefliger structure of codimension n. This step works on all manifolds, even closed. The seco…

Two Riemannian manifolds are said to have $C^k$-conjugate geodesic flows if there exist an $C^k$ diffeomorphism between their unit tangent bundles which intertwines the geodesic flows. We obtain a number of rigidity results for the geodesic flows on compact 2-step Riemannian nilmanifolds: For generic 2-step nilmanifold…

A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However, this shape has not yet been examined in detail. This work shows empirically that…

Paper presents a copula-based method to efficiently generate correlated sample paths from multi-step time series models.

Unified model improves sampling speed and quality.

We give a necessary and sufficient condition for $k$-step nilmanifolds associated with graphs $(k \geq 3)$ to admit Anosov automorphisms. We also prove nonexistence of Anosov automorphisms on certain classes of 2-step and 3-step nilmanifolds.

The paper explores dynamic ensembles for multi-step forecasting.

Study symplectic structures on low dimensional 2-step nilmanifolds.