Tata Institute of Fundamental Research
Universal Convexification via Risk Aversion
STCS Seminar
Speaker:
Dvijotham Krishnamurthy (Center for Mathematics of Information
California Institute of Technology
1200 E California Blvd
Pasadena, CA 91125 - 8000
United States of America)
Organiser:
Sandeep K Juneja
Date:
Friday, 7 Nov 2014, 14:30 to 15:30
Venue:
AG-66 (Lecture Theatre)
(Scan to add to calendar)
Abstract:
Abstract: We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and prove additive approximation guarantees. We then develop algorithms based on stochastic gradient methods to solve the resulting optimization problems and show bounds on convergence rates. We then extend this framework to apply to a general class of discrete-time dynamical systems. In this context, our convexification approach falls under the well-studied paradigm of risk-sensitive Markov Decision Processes. We derive the first known model-based and model-free policy gradient optimization algorithms with guaranteed convergence to the optimal solution. Finally, we present numerical results validating our formulation in different applications.
| Speaker: | Dvijotham Krishnamurthy (Center for Mathematics of Information California Institute of Technology 1200 E California Blvd Pasadena, CA 91125 - 8000 United States of America) |
| Organiser: | Sandeep K Juneja |
| Date: | Friday, 7 Nov 2014, 14:30 to 15:30 |
| Venue: | AG-66 (Lecture Theatre) |
(Scan to add to calendar)
Abstract:
Abstract: We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and prove additive approximation guarantees. We then develop algorithms based on stochastic gradient methods to solve the resulting optimization problems and show bounds on convergence rates. We then extend this framework to apply to a general class of discrete-time dynamical systems. In this context, our convexification approach falls under the well-studied paradigm of risk-sensitive Markov Decision Processes. We derive the first known model-based and model-free policy gradient optimization algorithms with guaranteed convergence to the optimal solution. Finally, we present numerical results validating our formulation in different applications.