We introduce the controlled predictive linear-Gaussian model (cPLG), a model that uses predictive state to model discrete-time dynamical systems with real-valued observations and vector-valued actions. This extends the PLG, an uncontrolled model recently introduced by Rudary et al. (2005). We show that the cPLG subsumes controlled linear dynamical systems (LDS, also called Kalman filter models) of equal dimension, but requires fewer parameters. We also introduce the predictive linear-quadratic Gaussian problem, a cost-minimization problem based on the cPLG that we show is equivalent to linear-quadratic Gaussian problems (LQG, sometimes called LQR). We present an algorithm to estimate cPLG parameters from data, and show that our algorithm is a consistent estimation procedure. Finally, we present empirical results suggesting that our algorithm performs favorably compared to expectation maximization on controlled LDS models.

Reminder systems support people with impaired prospective memory and/or executive function, by providing them with reminders of their functional daily activities. We integrate temporal constraint reasoning with reinforcement learning (RL) to build an adaptive reminder system and in a simulated environment demonstrate that it can personalize to a user and adapt to both short- and long-term changes. In addition to advancing the application domain, our integrated algorithm contributes to research on temporal constraint reasoning by showing how RL can select an optimal policy from amongst a set of temporally consistent ones, and it contributes to the work on RL by showing how temporal constraint reasoning can be used to dramatically reduce the space of actions from which an RL agent needs to learn.

Predictive state representations (PSRs) use predictions of a set of tests to represent the state of controlled dynamical systems. One reason why this representation is exciting as an alternative to partially observable Markov decision processes (POMDPs) is that PSR models of dynamical systems may be much more compact than POMDP models. Empirical work on PSRs to date has focused on linear PSRs, which have not allowed for compression relative to POMDPs. We introduce a new notion of tests which allows us to define a new type of PSR that is nonlinear in general and allows for exponential compression in some deterministic dynami- cal systems. These new tests, called e-tests, are related to the tests used by Rivest and Schapire [1] in their work with the diversity representation, but our PSR avoids some of the pitfalls of their representation—in partic- ular, its potential to be exponentially larger than the equivalent POMDP.