Overlapping Communities Detection via Measure Space Embedding

We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of $k$-means in that space is applied. The algorithm is therefore fast and easily parallelizable. We evaluate the algorithm on standard random graph benchmarks, including some overlapping community benchmarks, and find its performance to be better or at least as good as previously known algorithms. We also prove a linear time (in number of edges) guarantee for the algorithm on a $p,q$-stochastic block model with $p \geq c\cdot N^{-\frac{1}{2} + \epsilon}$ and $p-q \geq c' \sqrt{p N^{-\frac{1}{2} + \epsilon} \log N}$.

Bootstrapping Skills

The monolithic approach to policy representation in Markov Decision Processes (MDPs) looks for a single policy that can be represented as a function from states to actions. For the monolithic approach to succeed (and this is not always possible), a complex feature representation is often necessary since the policy is a complex object that has to prescribe what actions to take all over the state space. This is especially true in large domains with complicated dynamics. It is also computationally inefficient to both learn and plan in MDPs using a complex monolithic approach. We present a different approach where we restrict the policy space to policies that can be represented as combinations of simpler, parameterized skills---a type of temporally extended action, with a simple policy representation. We introduce Learning Skills via Bootstrapping (LSB) that can use a broad family of Reinforcement Learning (RL) algorithms as a "black box" to iteratively learn parametrized skills. Initially, the learned skills are short-sighted but each iteration of the algorithm allows the skills to bootstrap off one another, improving each skill in the process. We prove that this bootstrapping process returns a near-optimal policy. Furthermore, our experiments demonstrate that LSB can solve MDPs that, given the same representational power, could not be solved by a monolithic approach. Thus, planning with learned skills results in better policies without requiring complex policy representations.

Policy Gradient for Coherent Risk Measures

Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as the variance or conditional value at risk (CVaR). In this work, we extend the policy gradient method to the whole class of coherent risk measures, which is widely accepted in finance and operations research, among other fields. We consider both static and time-consistent dynamic risk measures. For static risk measures, our approach is in the spirit of policy gradient algorithms and combines a standard sampling approach with convex programming. For dynamic risk measures, our approach is actor-critic style and involves explicit approximation of value function. Most importantly, our contribution presents a unified approach to risk-sensitive reinforcement learning that generalizes and extends previous results.

Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach

In this paper we address the problem of decision making within a Markov decision process (MDP) framework where risk and modeling errors are taken into account. Our approach is to minimize a risk-sensitive conditional-value-at-risk (CVaR) objective, as opposed to a standard risk-neutral expectation. We refer to such problem as CVaR MDP. Our first contribution is to show that a CVaR objective, besides capturing risk sensitivity, has an alternative interpretation as expected cost under worst-case modeling errors, for a given error budget. This result, which is of independent interest, motivates CVaR MDPs as a unifying framework for risk-sensitive and robust decision making. Our second contribution is to present an approximate value-iteration algorithm for CVaR MDPs and analyze its convergence rate. To our knowledge, this is the first solution algorithm for CVaR MDPs that enjoys error guarantees. Finally, we present results from numerical experiments that corroborate our theoretical findings and show the practicality of our approach.

Overlapping Community Detection by Online Cluster Aggregation

We present a new online algorithm for detecting overlapping communities. The main ingredients are a modification of an online k-means algorithm and a new approach to modelling overlap in communities. An evaluation on large benchmark graphs shows that the quality of discovered communities compares favorably to several methods in the recent literature, while the running time is significantly improved.

Actively Learning to Attract Followers on Twitter

Twitter, a popular social network, presents great opportunities for on-line machine learning research. However, previous research has focused almost entirely on learning from passively collected data. We study the problem of learning to acquire followers through normative user behavior, as opposed to the mass following policies applied by many bots. We formalize the problem as a contextual bandit problem, in which we consider retweeting content to be the action chosen and each tweet (content) is accompanied by context. We design reward signals based on the change in followers. The result of our month long experiment with 60 agents suggests that (1) aggregating experience across agents can adversely impact prediction accuracy and (2) the Twitter community's response to different actions is non-stationary. Our findings suggest that actively learning on-line can provide deeper insights about how to attract followers than machine learning over passively collected data alone.

Thompson Sampling for Learning Parameterized Markov Decision Processes

We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a version of Thompson sampling for parameterized reinforcement learning problems, and derive a frequentist regret bound for priors over general parameter spaces. The result shows that the number of instants where suboptimal actions are chosen scales logarithmically with time, with high probability. It holds for prior distributions that put significant probability near the true model, without any additional, specific closed-form structure such as conjugate or product-form priors. The constant factor in the logarithmic scaling encodes the information complexity of learning the MDP in terms of the Kullback-Leibler geometry of the parameter space.

Off-policy evaluation for MDPs with unknown structure

Off-policy learning in dynamic decision problems is essential for providing strong evidence that a new policy is better than the one in use. But how can we prove superiority without testing the new policy? To answer this question, we introduce the G-SCOPE algorithm that evaluates a new policy based on data generated by the existing policy. Our algorithm is both computationally and sample efficient because it greedily learns to exploit factored structure in the dynamics of the environment. We present a finite sample analysis of our approach and show through experiments that the algorithm scales well on high-dimensional problems with few samples.

Contextual Markov Decision Processes

We consider a planning problem where the dynamics and rewards of the environment depend on a hidden static parameter referred to as the context. The objective is to learn a strategy that maximizes the accumulated reward across all contexts. The new model, called Contextual Markov Decision Process (CMDP), can model a customer's behavior when interacting with a website (the learner). The customer's behavior depends on gender, age, location, device, etc. Based on that behavior, the website objective is to determine customer characteristics, and to optimize the interaction between them. Our work focuses on one basic scenario--finite horizon with a small known number of possible contexts. We suggest a family of algorithms with provable guarantees that learn the underlying models and the latent contexts, and optimize the CMDPs. Bounds are obtained for specific naive implementations, and extensions of the framework are discussed, laying the ground for future research.

Distributed Robust Learning

We propose a framework for distributed robust statistical learning on {\em big contaminated data}. The Distributed Robust Learning (DRL) framework can reduce the computational time of traditional robust learning methods by several orders of magnitude. We analyze the robustness property of DRL, showing that DRL not only preserves the robustness of the base robust learning method, but also tolerates contaminations on a constant fraction of results from computing nodes (node failures). More precisely, even in presence of the most adversarial outlier distribution over computing nodes, DRL still achieves a breakdown point of at least $ \lambda^*/2 $, where $ \lambda^* $ is the break down point of corresponding centralized algorithm. This is in stark contrast with naive division-and-averaging implementation, which may reduce the breakdown point by a factor of $ k $ when $ k $ computing nodes are used. We then specialize the DRL framework for two concrete cases: distributed robust principal component analysis and distributed robust regression. We demonstrate the efficiency and the robustness advantages of DRL through comprehensive simulations and predicting image tags on a large-scale image set.