Model learning for switching linear systems with autonomous mode transitions

Abstract

Abstract-We present a novel method for model learning in hybrid discrete-continuous systems. The approach uses approximate Expectation-Maximization to learn the MaximumLikelihood parameters of a switching linear system. The approach extends previous work by 1) considering autonomous mode transitions, where the discrete transitions are conditioned on the continuous state, and 2) learning the effects of control inputs on the system. We evaluate the approach in simulation.

Beyond local optimality: An improved approach to hybrid model learning

“…This makes it difficult to use global or stochastic optimization techniques [17], [18], [19] that often rely on the ability to sample from the likelihood or its gradient. Previous work employs an approximation of the posterior distribution over the hidden state and uses local optimization techniques to learn the model parameters of hybrid systems [10], [14]. We extend [14] by avoiding convergence to a single local optima via a guided restart method over the parameter space; the algorithm aims to find globally or near-globally optimal solutions to the hybrid model learning problem.…”

“…One widely-used technique that has been adapted to learn the model parameters for these systems is Expectation Maximization [11], [12], [13], [10], [14]. Expectation Maximization (EM) is well-suited to this problem because it provides Maximum Likelihood parameter estimates from data where some variables may be unobservable, or hidden.…”

Planning in partially-observable switching-mode continuous domains

“…1a for an illustration). SSMs have been used to approximate the dynamics of a diverse set of complex systems, including planetary rover operation [1], honeybee dances [12] and the IBOVESPA stock index [5]. The bulk of prior work on SSMs has focused on inference in SSMs with hidden state or mode variables, or model parameter learning.…”

“…In order to model such systems which involve multi-modal, state-dependent dynamics we create a particular variant of an SSM that conditions the mode transitions on the previous continuous-state, similar to [1]. Figure 1b …”

“…Brooks et al [2] restrict the belief state to be a unimodal Gaussian, 1 and then plan by discretizing the Gaussian parameters and using Fitted Value Iteration over that representation. However, this approach will be limited in any domain that requires multi-modal beliefs to achieve good performance.…”