Optimization, Learning, and Games with Predictable Sequences

We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth functions, and apply the results to saddle-point type problems. Next, we prove that a version of Optimistic Mirror Descent (which has a close relation to the Exponential Weights algorithm) can be used by two strongly-uncoupled players in a finite zero-sum matrix game to converge to the minimax equilibrium at the rate of O((log T)/T). This addresses a question of Daskalakis et al 2011. Further, we consider a partial information version of the problem. We then apply the results to convex programming and exhibit a simple algorithm for the approximate Max Flow problem

Dynamic Variational Autoencoders for Visual Process Modeling

This work studies the problem of modeling visual processes by leveraging deep generative architectures for learning linear, Gaussian representations from observed sequences. We propose a joint learning framework, combining a vector autoregressive model and Variational Autoencoders. This results in an architecture that allows Variational Autoencoders to simultaneously learn a non-linear observation as well as a linear state model from sequences of frames. We validate our approach on artificial sequences and dynamic textures

Low-frequency oscillatory correlates of auditory predictive processing in cortical-subcortical networks: a MEG-study

Emerging evidence supports the role of neural oscillations as a mechanism for predictive information processing across large-scale networks. However, the oscillatory signatures underlying auditory mismatch detection and information flow between brain regions remain unclear. To address this issue, we examined the contribution of oscillatory activity at theta/alpha-bands (4–8/8–13 Hz) and assessed directed connectivity in magnetoencephalographic data while 17 human participants were presented with sound sequences containing predictable repetitions and order manipulations that elicited prediction-error responses. We characterized the spectro-temporal properties of neural generators using a minimum-norm approach and assessed directed connectivity using Granger Causality analysis. Mismatching sequences elicited increased theta power and phase-locking in auditory, hippocampal and prefrontal cortices, suggesting that theta-band oscillations underlie prediction-error generation in cortical-subcortical networks. Furthermore, enhanced feedforward theta/alpha-band connectivity was observed in auditory-prefrontal networks during mismatching sequences, while increased feedback connectivity in the alpha-band was observed between hippocampus and auditory regions during predictable sounds. Our findings highlight the involvement of hippocampal theta/alpha-band oscillations towards auditory prediction-error generation and suggest a spectral dissociation between inter-areal feedforward vs. feedback signalling, thus providing novel insights into the oscillatory mechanisms underlying auditory predictive processing