An official website of the United States government
Spin–Orbit Coupling and Admixture Coefficients in SA-CASSCF and MS-CASPT2, and Triplet Excitation Yield Simulated via Trajectory Surface Hopping and Calibrated SA-CASSCF in 1,2-Dioxetane Derivatives
- PAR ID:
- 10568140
- Publisher / Repository:
- American Chemical Society
- Date Published:
- Journal Name:
- The Journal of Physical Chemistry A
- Volume:
- 129
- Issue:
- 5
- ISSN:
- 1089-5639
- Format(s):
- Medium: X Size: p. 1195-1206
- Size(s):
- p. 1195-1206
- Sponsoring Org:
- National Science Foundation
More Like this
-
Motivated by Q-learning, we study nonsmooth contractive stochastic approximation (SA) with constant stepsize. We focus on two important classes of dynamics: 1) nonsmooth contractive SA with additive noise, and 2) synchronous and asynchronous Q-learning, which features both additive and multiplicative noise. For both dynamics, we establish weak convergence of the iterates to a stationary limit distribution in Wasserstein distance. Furthermore, we propose a prelimit coupling technique for establishing steady-state convergence and characterize the limit of the stationary distribution as the stepsize goes to zero. Using this result, we derive that the asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize, which stands in sharp contrast to smooth SA. This bias characterization allows for the use of Richardson-Romberg extrapolation for bias reduction in nonsmooth SA.more » « less
-
Motivated by Q-learning, we study nonsmooth contractive stochastic approximation (SA) with constant stepsize. We focus on two important classes of dynamics: 1) nonsmooth contractive SA with additive noise, and 2) synchronous and asynchronous Q-learning, which features both additive and multiplicative noise. For both dynamics, we establish weak convergence of the iterates to a stationary limit distribution in Wasserstein distance. Furthermore, we propose a prelimit coupling technique for establishing steady-state convergence and characterize the limit of the stationary distribution as the stepsize goes to zero. Using this result, we derive that the asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize, which stands in sharp contrast to smooth SA. This bias characterization allows for the use of Richardson-Romberg extrapolation for bias reduction in nonsmooth SA.more » « less
