Limits of Actor-Critic Algorithms for Decision Tree Policies Learning in IBMDPs

Interpretability of AI models allows for user safety checks to build trust in such AIs. In particular, Decision Trees (DTs) provide a global look at the learned model and transparently reveal which features of the input are critical for making a decision. However, interpretability is hindered if the DT is too large. To learn compact trees, a recent Reinforcement Learning (RL) framework has been proposed to explore the space of DTs using deep RL. This framework augments a decision problem (e.g. a supervised classification task) with additional actions that gather information about the features of an otherwise hidden input. By appropriately penalizing these actions, the agent learns to optimally trade-off size and performance of DTs. In practice, a reactive policy for a partially observable Markov decision process (MDP) needs to be learned, which is still an open problem. We show in this paper that deep RL can fail even on simple toy tasks of this class. However, when the underlying decision problem is a supervised classification task, we show that finding the optimal tree can be cast as a fully observable Markov decision problem and be solved efficiently, giving rise to a new family of algorithms for learning DTs that go beyond the classical greedy maximization ones.

Discovering the Interpretability-Performance Pareto Front of Decision Trees with Dynamic Programming

Decision trees are known to be intrinsically interpretable as they can be inspected and interpreted by humans. Furthermore, recent hardware advances have rekindled an interest for optimal decision tree algorithms, that produce more accurate trees than the usual greedy approaches. However, these optimal algorithms return a single tree optimizing a hand defined interpretability-performance trade-off, obtained by specifying a maximum number of decision nodes, giving no further insights about the quality of this trade-off. In this paper, we propose a new Markov Decision Problem (MDP) formulation for finding optimal decision trees. The main interest of this formulation is that we can compute the optimal decision trees for several interpretability-performance trade-offs by solving a single dynamic program, letting the user choose a posteriori the tree that best suits their needs. Empirically, we show that our method is competitive with state-of-the-art algorithms in terms of accuracy and runtime while returning a whole set of trees on the interpretability-performance Pareto front.

Optimal Interpretability-Performance Trade-off of Classification Trees with Black-Box Reinforcement Learning

Interpretability of AI models allows for user safety checks to build trust in these models. In particular, decision trees (DTs) provide a global view on the learned model and clearly outlines the role of the features that are critical to classify a given data. However, interpretability is hindered if the DT is too large. To learn compact trees, a Reinforcement Learning (RL) framework has been recently proposed to explore the space of DTs. A given supervised classification task is modeled as a Markov decision problem (MDP) and then augmented with additional actions that gather information about the features, equivalent to building a DT. By appropriately penalizing these actions, the RL agent learns to optimally trade-off size and performance of a DT. However, to do so, this RL agent has to solve a partially observable MDP. The main contribution of this paper is to prove that it is sufficient to solve a fully observable problem to learn a DT optimizing the interpretability-performance trade-off. As such any planning or RL algorithm can be used. We demonstrate the effectiveness of this approach on a set of classical supervised classification datasets and compare our approach with other interpretability-performance optimizing methods.

Entropy Regularized Reinforcement Learning with Cascading Networks

Deep Reinforcement Learning (Deep RL) has had incredible achievements on high dimensional problems, yet its learning process remains unstable even on the simplest tasks. Deep RL uses neural networks as function approximators. These neural models are largely inspired by developments in the (un)supervised machine learning community. Compared to these learning frameworks, one of the major difficulties of RL is the absence of i.i.d. data. One way to cope with this difficulty is to control the rate of change of the policy at every iteration. In this work, we challenge the common practices of the (un)supervised learning community of using a fixed neural architecture, by having a neural model that grows in size at each policy update. This allows a closed form entropy regularized policy update, which leads to a better control of the rate of change of the policy at each iteration and help cope with the non i.i.d. nature of RL. Initial experiments on classical RL benchmarks show promising results with remarkable convergence on some RL tasks when compared to other deep RL baselines, while exhibiting limitations on others.

Convex Optimization with an Interpolation-based Projection and its Application to Deep Learning

Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these convex layers are significantly more expensive to compute than those of a typical neural network. We investigate in this paper whether an inexact, but cheaper projection, can drive a descent algorithm to an optimum. Specifically, we propose an interpolation-based projection that is computationally cheap and easy to compute given a convex, domain defining, function. We then propose an optimization algorithm that follows the gradient of the composition of the objective and the projection and prove its convergence for linear objectives and arbitrary convex and Lipschitz domain defining inequality constraints. In addition to the theoretical contributions, we demonstrate empirically the practical interest of the interpolation projection when used in conjunction with neural networks in a reinforcement learning and a supervised learning setting.

Reinforcement Learning from a Mixture of Interpretable Experts

Reinforcement learning (RL) has demonstrated its ability to solve high dimensional tasks by leveraging non-linear function approximators. These successes however are mostly achieved by 'black-box' policies in simulated domains. When deploying RL to the real world, several concerns regarding the use of a 'black-box' policy might be raised. In an effort to make the policies learned by RL more transparent, we propose in this paper a policy iteration scheme that retains a complex function approximator for its internal value predictions but constrains the policy to have a concise, hierarchical, and human-readable structure, based on a mixture of interpretable experts. We show that our proposed algorithm can learn compelling policies on continuous action deep RL benchmarks, matching the performance of neural network based policies, but returns policies that are more amenable to human inspection than neural network or linear-in-feature policies.

An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions

The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in a number of related literature. However, Rosenblatt's analysis is only valid for infinitesimal bandwidth. In contrast, we propose in this paper an upper bound of the bias which holds for finite bandwidths. Moreover, contrarily to the classic analysis we allow for discontinuous first order derivative of the regression function, we extend our bounds for multidimensional domains and we include the knowledge of the bound of the regression function when it exists and if it is known, to obtain a tighter bound. We believe that this work has potential applications in those fields where some hard guarantees on the error are needed

Compatible Natural Gradient Policy Search

Trust-region methods have yielded state-of-the-art results in policy search. A common approach is to use KL-divergence to bound the region of trust resulting in a natural gradient policy update. We show that the natural gradient and trust region optimization are equivalent if we use the natural parameterization of a standard exponential policy distribution in combination with compatible value function approximation. Moreover, we show that standard natural gradient updates may reduce the entropy of the policy according to a wrong schedule leading to premature convergence. To control entropy reduction we introduce a new policy search method called compatible policy search (COPOS) which bounds entropy loss. The experimental results show that COPOS yields state-of-the-art results in challenging continuous control tasks and in discrete partially observable tasks.

Model-Free Trajectory-based Policy Optimization with Monotonic Improvement

Many of the recent trajectory optimization algorithms alternate between linear approximation of the system dynamics around the mean trajectory and conservative policy update. One way of constraining the policy change is by bounding the Kullback-Leibler (KL) divergence between successive policies. These approaches already demonstrated great experimental success in challenging problems such as end-to-end control of physical systems. However, the linear approximation of the system dynamics can introduce a bias in the policy update and prevent convergence to the optimal policy. In this article, we propose a new model-free trajectory-based policy optimization algorithm with guaranteed monotonic improvement. The algorithm backpropagates a local, quadratic and time-dependent \qfunc~learned from trajectory data instead of a model of the system dynamics. Our policy update ensures exact KL-constraint satisfaction without simplifying assumptions on the system dynamics. We experimentally demonstrate on highly non-linear control tasks the improvement in performance of our algorithm in comparison to approaches linearizing the system dynamics. In order to show the monotonic improvement of our algorithm, we additionally conduct a theoretical analysis of our policy update scheme to derive a lower bound of the change in policy return between successive iterations.

APRIL: Active Preference-learning based Reinforcement Learning

This paper focuses on reinforcement learning (RL) with limited prior knowledge. In the domain of swarm robotics for instance, the expert can hardly design a reward function or demonstrate the target behavior, forbidding the use of both standard RL and inverse reinforcement learning. Although with a limited expertise, the human expert is still often able to emit preferences and rank the agent demonstrations. Earlier work has presented an iterative preference-based RL framework: expert preferences are exploited to learn an approximate policy return, thus enabling the agent to achieve direct policy search. Iteratively, the agent selects a new candidate policy and demonstrates it; the expert ranks the new demonstration comparatively to the previous best one; the expert's ranking feedback enables the agent to refine the approximate policy return, and the process is iterated. In this paper, preference-based reinforcement learning is combined with active ranking in order to decrease the number of ranking queries to the expert needed to yield a satisfactory policy. Experiments on the mountain car and the cancer treatment testbeds witness that a couple of dozen rankings enable to learn a competent policy.