Policy Optimization of Finite-Horizon Kalman Filter with Unknown Noise Covariance

This paper is on learning the Kalman gain by policy optimization method. Firstly, we reformulate the finite-horizon Kalman filter as a policy optimization problem of the dual system. Secondly, we obtain the global linear convergence of exact gradient descent method in the setting of known parameters. Thirdly, the gradient estimation and stochastic gradient descent method are proposed to solve the policy optimization problem, and further the global linear convergence and sample complexity of stochastic gradient descent are provided for the setting of unknown noise covariance matrices and known model parameters

Continuous-time Mean-Variance Portfolio Selection with Stochastic Parameters

This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a bond. In the considered model firstly proposed by [3], the mean returns of individual assets are explicitly affected by underlying Gaussian economic factors. Using past and present information of the asset prices, a partial-information stochastic optimal control problem with random coefficients is formulated. Here, the partial information is due to the fact that the economic factors can not be directly observed. Via dynamic programming theory, the optimal portfolio strategy can be constructed by solving a deterministic forward Riccati-type ordinary differential equation and two linear deterministic backward ordinary differential equations

Solving Coupled Nonlinear Forward-backward Stochastic Differential Equations: An Optimization Perspective with Backward Measurability Loss

This paper aims to extend the BML method proposed in Wang et al. [22] to make it applicable to more general coupled nonlinear FBSDEs. We interpret BML from the fixed-point iteration perspective and show that optimizing BML is equivalent to minimizing the distance between two consecutive trial solutions in a fixed-point iteration. Thus, this paper provides a theoretical foundation for an optimization-based approach to solving FBSDEs. We also empirically evaluate the method through four numerical experiments

Tracing blastomere fate choices of early embryos in single cell culture

Blastomeres of early vertebrate embryos undergo numerous fate choices for division, motility, pluripotency maintenance and restriction culminating in various cell lineages. Tracing blastomere fate choices at the single cell level in vitro has not been possible because of the inability to isolate and cultivate early blastomeres as single cells. Here we report the establishment of single cell culture system in the fish medaka, enabling the isolation and cultivation of individual blastomeres from 16- to 64-cell embryos for fate tracing at the single cell level in vitro. Interestingly, these blastomeres immediately upon isolation exhibit motility, lose synchronous divisions and even stop dividing in ≥50% cases, suggesting that the widely accepted nucleocytoplasmic ratio controlling synchronous divisions in entire embryos does not operate on individual blastomeres. We even observed abortive division, endomitosis and cell fusion. Strikingly, ~5% of blastomeres in single cell culture generated extraembryonic yolk syncytial cells, embryonic stem cells and neural crest-derived pigment cells with timings mimicking their appearance in embryos. We revealed the maternal inheritance of key lineage regulators and their differential expression in cleavage embryos. Therefore, medaka blastomeres possess the accessibility for single cell culture, previously unidentified heterogeneity in motility, division, gene expression and intrinsic ability to generate major extraembryonic and embryonic lineages without positioning cues. Our data demonstrate the fidelity and potential of the single cell culture system for tracking blastomere fate decisions under defined conditions in vitro