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Title: Understanding the Relation Between Maximum-Entropy Inverse Reinforcement Learning and Behaviour Cloning

Paper content:
In many settings, it is desirable to learn decision-making and control policies through learning or from expert demonstrations.
The most common approaches under this framework are Behaviour Cloning (BC), and Inverse Reinforcement Learning (IRL).
Recent methods for IRL have demonstrated the capacity to learn effective policies with access to a very limited set of demonstrations, a scenario in which BC methods often fail.
Unfortunately, directly comparing the algorithms for these methods does not provide adequate intuition for understanding this difference in performance.
This is the motivating factor for our work.
We begin by presenting $f$-MAX, a generalization of AIRL (Fu et al., 2018), a state-of-the-art IRL method.
$f$-MAX provides grounds for more directly comparing the objectives for LfD.
We demonstrate that $f$-MAX, and by inheritance AIRL, is a subset of the cost-regularized IRL framework laid out by Ho & Ermon (2016).
We conclude by empirically evaluating the factors of difference between various LfD objectives in the continuous control domain.
Modern advances in reinforcement learning aim to alleviate the need for hand-engineered decisionmaking and control algorithms by designing general purpose methods that learn to optimize provided reward functions.
In many cases however, it is either too challenging to optimize a given reward (e.g. due to sparsity of signal), or it is simply impossible to design a reward function that captures the intricate details of desired outcomes.
One approach to overcoming such hurdles is Learning from Demonstrations (LfD), where algorithms are provided with expert demonstrations of how to accomplish desired tasks.The most common approaches in the LfD framework are Behaviour Cloning (BC) and Inverse Reinforcement Learning (IRL) BID22 BID15 .
In standard BC, learning from demonstrations is treated as a supervised learning problem and policies are trained to regress expert actions from a dataset of expert demonstrations.
Other forms of Behaviour Cloning, such as DAgger BID21 , consider how to make use of an expert in a more optimal fashion.
On the other hand, in IRL the aim is to infer the reward function of the expert, and subsequently train a policy to optimize this reward.
The motivation for IRL stems from the intuition that the reward function is the most concise and portable representation of a task BID15 BID0 .Unfortunately
, the standard IRL formulation BID15 faces degeneracy issues 1 . A successful
framework for overcoming such challenges is the Maximum-Entropy (Max-Ent) IRL method BID28 BID27 . A line of research
stemming from the Max-Ent IRL framework has lead to recent "adversarial" methods BID12 BID4 BID7 1 for example, any policy is optimal for the constant reward function r(s, a) = 0 2 BACKGROUND
The motivation for this work stemmed from the superior performance of recent direct Max-Ent IRL methods BID12 BID7 compared to BC in the low-data regime, and the desire to understand the relation between various approaches for Learning from Demonstrations.
We first presented f -MAX, a generalization of AIRL BID7 , which allowed us to interpret AIRL as optimizing for KL (ρ π (s, a)||ρ exp (s, a)).
We demonstrated that f -MAX, and by inhertance AIRL, is a subset of the cost-regularized IRL framework laid out by BID12 .
Comparing to the standard BC objective, E ρ exp (s) [KL (ρ exp (a|s)||ρ π (a|s))], we hypothesized two reasons for the superior performance of AIRL:
1) the additional terms in the objective encouraging the matching of marginal state distributions, and
2) the direction of the KL divergence being optimized.
Setting out to empirically evaluate these claims we presented FAIRL, a one-line modification of the AIRL algorithm that optimizes KL (ρ exp (s, a)||ρ π (s, a)).
FAIRL outperformed BC in a similar fashion to AIRL, which allowed us to conclude the key factor being the matching of state marginals.
Additional comparisons between FAIRL and AIRL provided initial understanding about the role of the direction of the KL being optimized.
In future work we aim to produce results on a more diverse set of more challenging environments.
Additionally, evaluating other choices of f -divergence beyond forward and reverse KL may present interesting avenues for improvement BID26 .
Lastly, but importantly, we would like to understand whether the mode-covering behaviour of FAIRL could result in more robust policies BID19 .A
SOME USEFUL IDENTITIES Let h : S × A → R be an arbitrary function. If
all episodes have the same length T , we have, DISPLAYFORM0 DISPLAYFORM1 In a somewhat similar fashion, in the infinite horizon case with fixed probability γ ∈ (0, 1)
of transitioning to a terminal state, for the discounted sum below we have, DISPLAYFORM2 DISPLAYFORM3 where Γ := 1 1−γ is the normalizer of the sum t γ t . Since
the integral of an infinite series is not always equal to the infinite series of integrals, some analytic considerations must be made to go from equation 34 to 35. But,
one simple case in which it holds is when the ranges of h and all ρ π (s t , a t ) are bounded.

assistant: text: Distribution matching through divergence minimization provides a common ground for comparing adversarial Maximum-Entropy Inverse Reinforcement Learning methods to Behaviour Cloning.