Nicolas Le Roux

Anytime Tail Averaging

Tail averaging consists in averaging the last examples in a stream. Common techniques either have a memory requirement which grows with the … (see more)number of samples to average, are not available at every timestep or do not accomodate growing windows. We propose two techniques with a low constant memory cost that perform tail averaging with access to the average at every time step. We also show how one can improve the accuracy of that average at the cost of increased memory consumption.

2019-02-13

ArXiv (preprint)

Distributional reinforcement learning with linear function approximation

Subhodeep Moitra

Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited.… (see more) One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cramer distance, but their results only apply to the tabular setting and ignore C51's use of a softmax to produce normalized distributions. In this paper we adapt the Cramer distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cramer-based and can be combined to linear function approximation, with formal guarantees in the context of policy evaluation. In allowing the model's prediction to be any real vector, we lose the probabilistic interpretation behind the method, but otherwise maintain the appealing properties of distributional approaches. To the best of our knowledge, ours is the first proof of convergence of a distributional algorithm combined with function approximation. Perhaps surprisingly, our results provide evidence that Cramer-based distributional methods may perform worse than directly approximating the value function.

2019-02-08

ArXiv (preprint)

Distributional reinforcement learning with linear function approximation

Subhodeep Moitra

Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited.… (see more) One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cramer distance, but their results only apply to the tabular setting and ignore C51's use of a softmax to produce normalized distributions. In this paper we adapt the Cramer distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cramer-based and can be combined to linear function approximation, with formal guarantees in the context of policy evaluation. In allowing the model's prediction to be any real vector, we lose the probabilistic interpretation behind the method, but otherwise maintain the appealing properties of distributional approaches. To the best of our knowledge, ours is the first proof of convergence of a distributional algorithm combined with function approximation. Perhaps surprisingly, our results provide evidence that Cramer-based distributional methods may perform worse than directly approximating the value function.

2019-02-08

ArXiv (preprint)

A Geometric Perspective on Optimal Representations for Reinforcement Learning

Will Dabney

Robert Dadashi

Adrien Ali Taiga

Dale Eric. Schuurmans

Tor Lattimore

Clare Lyle

We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functi… (see more)ons. We leverage this perspective to provide formal evidence regarding the usefulness of value functions as auxiliary tasks. Our formulation considers adapting the representation to minimize the (linear) approximation of the value function of all stationary policies for a given environment. We show that this optimization reduces to making accurate predictions regarding a special class of value functions which we call adversarial value functions (AVFs). We demonstrate that using value functions as auxiliary tasks corresponds to an expected-error relaxation of our formulation, with AVFs a natural candidate, and identify a close relationship with proto-value functions (Mahadevan, 2005). We highlight characteristics of AVFs and their usefulness as auxiliary tasks in a series of experiments on the four-room domain.

2019-01-31

ArXiv (preprint)

A Geometric Perspective on Optimal Representations for Reinforcement Learning

Will Dabney

Robert Dadashi

Adrien Ali Taiga

Dale Schuurmans

Tor Lattimore

Clare Lyle

We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functi… (see more)ons. We leverage this perspective to provide formal evidence regarding the usefulness of value functions as auxiliary tasks. Our formulation considers adapting the representation to minimize the (linear) approximation of the value function of all stationary policies for a given environment. We show that this optimization reduces to making accurate predictions regarding a special class of value functions which we call adversarial value functions (AVFs). We demonstrate that using value functions as auxiliary tasks corresponds to an expected-error relaxation of our formulation, with AVFs a natural candidate, and identify a close relationship with proto-value functions (Mahadevan, 2005). We highlight characteristics of AVFs and their usefulness as auxiliary tasks in a series of experiments on the four-room domain.

A Geometric Perspective on Optimal Representations for Reinforcement Learning

Will Dabney

Robert Dadashi

Adrien Ali Taiga

Dale Schuurmans

Tor Lattimore

Clare Lyle

openreview.net

Reducing the variance in online optimization by transporting past gradients

Sébastien M. R. Arnold

Pierre-Antoine Manzagol

Reza Babanezhad Harikandeh

Ioannis Mitliagkas

Most stochastic optimization methods use gradients once before discarding them. While variance reduction methods have shown that reusing pas… (see more)t gradients can be beneficial when there is a finite number of datapoints, they do not easily extend to the online setting. One issue is the staleness due to using past gradients. We propose to correct this staleness using the idea of implicit gradient transport (IGT) which transforms gradients computed at previous iterates into gradients evaluated at the current iterate without using the Hessian explicitly. In addition to reducing the variance and bias of our updates over time, IGT can be used as a drop-in replacement for the gradient estimate in a number of well-understood methods such as heavy ball or Adam. We show experimentally that it achieves state-of-the-art results on a wide range of architectures and benchmarks. Additionally, the IGT gradient estimator yields the optimal asymptotic convergence rate for online stochastic optimization in the restricted setting where the Hessians of all component functions are equal.

Understanding the impact of entropy in policy learning

Zafarali Ahmed

Mohammad Norouzi

Dale Schuurmans

Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with \emph{explorat… (see more)ion} by encouraging the selection of more stochastic policies. In this work, we analyze this claim using new visualizations of the optimization landscape based on randomly perturbing the loss function. We first show that even with access to the exact gradient, policy optimization is difficult due to the geometry of the objective function. Then, we qualitatively show that in some environments, a policy with higher entropy can make the optimization landscape smoother, thereby connecting local optima and enabling the use of larger learning rates. This paper presents new tools for understanding the optimization landscape, shows that policy entropy serves as a regularizer, and highlights the challenge of designing general-purpose policy optimization algorithms.

2018-11-27

(published)

www.semanticscholar.org

Combining adaptive algorithms and hypergradient method: a performance and robustness study

Akram Erraqabi

2018-09-27

(published)

www.semanticscholar.org

Online Hyper-Parameter Optimization

Damien Vincent

Sylvain Gelly

Olivier Bousquet

2018-02-15

(published)

openreview.net

Online variance-reducing optimization