Symbolic Methods for Hybrid Inference, Optimization, and Decision-Making
To date, our ability to perform exact closed-form inference or optimization in hybrid domains (that is, containing mixed discrete and continuous variables) is largely limited to special well-behaved cases. However, I argue that with an appropriate representation and data structure, we can vastly expand the class of models for which we can perform exact, closed-form inference.
In this talk, I review the algebraic decision diagram (ADD) and introduce an extension to continuous variables — termed the extended ADD (XADD) — to represent arbitrary piecewise functions over discrete and continuous variables and show how to efficiently compute elementary arithmetic operations, integrals, and maximization for these functions. Then I cover a wide range of novel applications where the XADD may be applied in expressive hybrid models: (1) exact learning and inference in expressive discrete and continuous variable graphical models, (2) factored, parameterized linear and quadratic optimization, and (3) exact solutions to continuous state, action, and observation MDPs and POMDPs.