A Bismut–Elworthy inequality for a Wasserstein diffusion on the circle

We introduce in this paper a strategy to prove gradient estimates for some infinite-dimensional diffusions on $$L_2$$ L 2 -Wasserstein spaces. For a specific example of a diffusion on the $$L_2$$ L 2 -Wasserstein space of the torus, we get a Bismut-Elworthy-Li formula up to a remainder term and deduce a gradient estimate with a rate of blow-up of order $$\mathcal O(t^{-(2+\varepsilon )})$$ O ( t - ( 2 + ε ) ) .

Complete Gradient Estimates of Quantum Markov Semigroups

In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.

Hindsight Value Function for Variance Reduction in Stochastic Dynamic Environment

Policy gradient methods are appealing in deep reinforcement learning but suffer from high variance of gradient estimate. To reduce the variance, the state value function is applied commonly. However, the effect of the state value function becomes limited in stochastic dynamic environments, where the unexpected state dynamics and rewards will increase the variance. In this paper, we propose to replace the state value function with a novel hindsight value function, which leverages the information from the future to reduce the variance of the gradient estimate for stochastic dynamic environments. Particularly, to obtain an ideally unbiased gradient estimate, we propose an information-theoretic approach, which optimizes the embeddings of the future to be independent of previous actions. In our experiments, we apply the proposed hindsight value function in stochastic dynamic environments, including discrete-action environments and continuous-action environments. Compared with the standard state value function, the proposed hindsight value function consistently reduces the variance, stabilizes the training, and improves the eventual policy.

Gradient estimate for the forward conjugate heat equation of forms under the Ricci flow

We establish bounds for the gradient of solutions to the forward conjugate heat equation of differential forms on a Riemannian manifold with the metric evolves under the Ricci flow.

Memory-Dependent Forecasting of COVID-19: The Flexibility of Extrapolated Kernel Least Mean Square Algorithm

The extrapolated kernel least mean square algorithm (extrap-KLMS) with memory is proposed for the forecasting of future trends of COVID-19. The extrap-KLMS is derived in the framework of data-driven modelling that attempts to describe the dynamics of infectious disease by reconstructing the phase-space of the state variables in a reproducing kernel Hilbert space (RKHS). Short-time forecasting is enabled via an extrapolation of the KLMS trained model using a forward euler step, along the direction of a memory-dependent gradient estimate. A user-defined memory averaging window allows users to incorporate prior knowledge of the history of the pandemic into the gradient estimate thus providing a spectrum of scenario-based estimates of futures trends. The performance of the extrap-KLMS method is validated using data set for Malaysia, Saudi Arabia and Italy in which we highlight the flexibility of the method in capturing persistent trends of the pandemic. A situational analysis of the Malaysian third wave further demonstrate the capabilities of our method

Memory-Dependent Forecasting of COVID-19: The Flexibility of Extrapolated Kernel Least Mean Square Algorithm

The extrapolated kernel least mean square algorithm (extrap-KLMS) with memory is proposed for the forecasting of future trends of COVID-19. The extrap-KLMS is derived in the framework of data-driven modelling that attempts to describe the dynamics of infectious disease by reconstructing the phase-space of the state variables in a reproducing kernel Hilbert space (RKHS). Short-time forecasting is enabled via an extrapolation of the KLMS trained model using a forward euler step, along the direction of a memory-dependent gradient estimate. A user-defined memory averaging window allows users to incorporate prior knowledge of the history of the pandemic into the gradient estimate thus providing a spectrum of scenario-based estimates of futures trends. The performance of the extrap-KLMS method is validated using data set for Malaysia, Saudi Arabia and Italy in which we highlight the flexibility of the method in capturing persistent trends of the pandemic. A situational analysis of the Malaysian third wave further demonstrate the capabilities of our method