Two Optimal Strategies for Active Learning of Causal Models from Interventional Data

From observational data alone, a causal DAG is only identifiable up to Markov equivalence. Interventional data generally improves identifiability; however, the gain of an intervention strongly depends on the intervention target, that is, the intervened variables. We present active learning (that is, optimal experimental design) strategies calculating optimal interventions for two different learning goals. The first one is a greedy approach using single-vertex interventions that maximizes the number of edges that can be oriented after each intervention. The second one yields in polynomial time a minimum set of targets of arbitrary size that guarantees full identifiability. This second approach proves a conjecture of Eberhardt (2008) indicating the number of unbounded intervention targets which is sufficient and in the worst case necessary for full identifiability. In a simulation study, we compare our two active learning approaches to random interventions and an existing approach, and analyze the influence of estimation errors on the overall performance of active learning

Learning Task Specifications from Demonstrations

Real world applications often naturally decompose into several sub-tasks. In many settings (e.g., robotics) demonstrations provide a natural way to specify the sub-tasks. However, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the sub-tasks can be safely recombined or limit the types of composition available. Motivated by this deficit, we consider the problem of inferring Boolean non-Markovian rewards (also known as logical trace properties or specifications) from demonstrations provided by an agent operating in an uncertain, stochastic environment. Crucially, specifications admit well-defined composition rules that are typically easy to interpret. In this paper, we formulate the specification inference task as a maximum a posteriori (MAP) probability inference problem, apply the principle of maximum entropy to derive an analytic demonstration likelihood model and give an efficient approach to search for the most likely specification in a large candidate pool of specifications. In our experiments, we demonstrate how learning specifications can help avoid common problems that often arise due to ad-hoc reward composition.Comment: NIPS 201

A Graph-Based Reinforcement Learning Method with Converged State Exploration and Exploitation

In any classical value-based reinforcement learning method, an agent, despite of its continuous interactions with the environment, is yet unable to quickly generate a complete and independent description of the entire environment, leaving the learning method to struggle with a difficult dilemma of choosing between the two tasks, namely exploration and exploitation. This problem becomes more pronounced when the agent has to deal with a dynamic environment, of which the configuration and/or parameters are constantly changing. In this paper, this problem is approached by first mapping a reinforcement learning scheme to a directed graph, and the set that contains all the states already explored shall continue to be exploited in the context of such a graph. We have proved that the two tasks of exploration and exploitation eventually converge in the decision-making process, and thus, there is no need to face the exploration vs. exploitation tradeoff as all the existing reinforcement learning methods do. Rather this observation indicates that a reinforcement learning scheme is essentially the same as searching for the shortest path in a dynamic environment, which is readily tackled by a modified Floyd-Warshall algorithm as proposed in the paper. The experimental results have confirmed that the proposed graph-based reinforcement learning algorithm has significantly higher performance than both standard Q-learning algorithm and improved Q-learning algorithm in solving mazes, rendering it an algorithm of choice in applications involving dynamic environments

Efficient First Order Methods for Linear Composite Regularizers

A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function \omega with a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and many more. In this paper, we present a general approach for computing the proximity operator of this class of regularizers, under the assumption that the proximity operator of the function \omega is known in advance. Our approach builds on a recent line of research on optimal first order optimization methods and uses fixed point iterations for numerically computing the proximity operator. It is more general than current approaches and, as we show with numerical simulations, computationally more efficient than available first order methods which do not achieve the optimal rate. In particular, our method outperforms state of the art O(1/T) methods for overlapping Group Lasso and matches optimal O(1/T^2) methods for the Fused Lasso and tree structured Group Lasso.Comment: 19 pages, 8 figure