Ross, S. and Bagnell, D.

in: JMLR W&CP 9: AISTATS 2010, pp. 661–668, *2010*

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### Abstract

Imitation Learning, while applied successfully on many large real-world problems, is typically addressed as a standard supervised learning problem, where it is assumed the training and testing data are i.i.d.. This is not true in imitation learning as the learned policy influences the future test inputs (states) upon which it will be tested. We show that this leads to compounding errors and a regret bound that grows quadratically in the time horizon of the task. We propose two alternative algorithms for imitation learning where training occurs over several episodes of interaction. These two approaches share in common that the learner’s policy is slowly modified from executing the expert’s policy to the learned policy. We show that this leads to stronger performance guarantees and demonstrate the improved performance on two challenging problems: training a learner to play 1) a 3D racing game (Super Tux Kart) and 2) Mario Bros.; given input images from the games and corresponding actions taken by a human expert and near-optimal planner respectively.

### Review

The authors note that previous approaches of learning a policy from an example policy are limited in the sense that they only see successful examples generated from the desired policy and, therefore, will exhibit a larger error than expected from supervised learning of independent samples, because an error can propagate through the series of decisions, if the policy hasn’t learnt to recover to the desired policy when an error occurred. They then show that a lower error can be expected when a Forward Algorithm is used for training which learns a non-stationary policy successively for each time step. The idea probably being (I’m not too sure) that the data at the time step that is currently learnt contains the errors (that lead to different states) you would usually expect from the learnt policies, because for every time step new data is sampled based on the already learnt policies. They transfer this idea to learning of a stationary policy and propose SMILe (stochastic mixing iterative learning). In this algorithm the stationary policy is a linear combination of policies learnt in previous iterations where the initial policy is the desired one. The influence of the desired policy decreases exponentially with the number of iterations, but also the weights of policies learnt later decrease exponentially, but stay fixed in subsequent iterations, i.e. the policies learnt first will have the largest weights eventually. This makes sense, because they will most probably be closest to the desired policy (seeing mostly samples produced from the desired policy).

The aim is to make the learnt policy more robust without using too many samples from the desired policy. I really wonder whether you could achieve exactly the same performance by simply additionally sampling the desired policy from randomly perturbed states and adding these as training points to learning of a single policy. Depending on how expensive your learning algorithm is this may be much faster in total (as you only have to learn once on a larger data set). Of course, you then may not have the theoretical guarantees provided in the paper. Another drawback of the approach presented in the paper is that it needs to be possible to sample from the desired policy interactively during the learning. I can’t imagine a scenario where this is practical (a human in the loop?).

I was interested in this, because in an extended abstract to a workshop (see attached files) the authors referred to this approach and also mentioned Langford2009 as a similar learning approach based on local updates. Also you can see the policy as a differential equation, i.e. the results of the paper may also apply to learning of dynamical systems without control inputs. The problems are certainly very similar.

They use a neural network to learn policies in the particular application they consider.