We consider learning the structures of Gaussian latent tree models with vector observations when a subset of them are arbitrarily corrupted. First, we present the sample complexities of Recursive Grouping (RG) and Chow-Liu Recursive Grouping (CLRG) without the assumption that the effective depth is bounded in the number of observed nodes, significantly generalizing the results in Choi et al. (2011). We show that Chow-Liu initialization in CLRG greatly reduces the sample complexity of RG from being exponential in the diameter of the tree to only logarithmic in the diameter for the hidden Markov model (HMM). Second, we robustify RG, CLRG, Neighbor Joining (NJ) and Spectral NJ (SNJ) by using the truncated inner product. These robustified algorithms can tolerate a number of corruptions up to the square root of the number of clean samples. Finally, we derive the first known instance-dependent impossibility result for structure learning of latent trees. The optimalities of the robust version of CLRG and NJ are verified by comparing their sample complexities and the impossibility result.

The success of reinforcement learning (RL) algorithms in large-scale, complex tasks depends on forming useful representations of the environment with which the algorithms interact. Feature selection and feature learning has long been an important subdomain of RL, and with the advent of deep reinforcement learning there has been much recent interest in understanding and improving the representations learnt by RL agents. Much of the work in representation learning has taken place from the perspective of auxiliary tasks [Jaderberg et al., 2017, Bellemare et al., 2017, Fedus et al., 2019]; in addition to the primary reinforcement learning task, the agent may attempt to predict and control additional aspects of the environment. Auxiliary tasks shape the agent's representation of the environment implicitly, typically via gradient descent on the additional learning objectives. As such, while auxiliary tasks continue to play an important role in improving the performance of deep RL algorithms, our understanding of the effects of auxiliary tasks on representations in RL is still in its infancy.

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation of Laplacian. Then, we cover the cuts of graph and spectral clustering which applies clustering in a subspace of data. Different optimization variants of Laplacian eigenmap and its out-of-sample extension are explained. Thereafter, we introduce the locality preserving projection and its kernel variant as linear special cases of Laplacian eigenmap. Versions of graph embedding are then explained which are generalized versions of Laplacian eigenmap and locality preserving projection. Finally, diffusion map is introduced which is a method based on Laplacian of data and random walks on the data graph.

The simple gesture of pointing can greatly augment ones ability to comprehend states of the world based on observations. It triggers additional inferences relevant to ones task at hand. We model an agents update to its belief of the world based on individual observations using a partially observable Markov decision process (POMDP), a mainstream artificial intelligence (AI) model of how to act rationally according to beliefs formed through observation. On top of that, we model pointing as a communicative act between agents who have a mutual understanding that the pointed observation must be relevant and interpretable. Our model measures relevance by defining a Smithian Value of Information (SVI) as the utility improvement of the POMDP agent before and after receiving the pointing. We model that agents calculate SVI by using the cognitive theory of Smithian helping as a principle of coordinating separate beliefs for action prediction and action evaluation. We then import SVI into rational speech act (RSA) as the utility function of an utterance. These lead us to a pragmatic model of pointing allowing for contextually flexible interpretations. We demonstrate the power of our Smithian pointing model by extending the Wumpus world, a classic AI task where a hunter hunts a monster with only partial observability of the world. We add another agent as a guide who can only help by marking an observation already perceived by the hunter with a pointing or not, without providing new observations or offering any instrumental help. Our results show that this severely limited and overloaded communication nevertheless significantly improves the hunters performance. The advantage of pointing is indeed due to a computation of relevance based on Smithian helping, as it disappears completely when the task is too difficult or too easy for the guide to help.

In this paper we present a novel method for learning hierarchical representations of Markov decision processes. Our method works by partitioning the state space into subsets, and defines subtasks for performing transitions between the partitions. We formulate the problem of partitioning the state space as an optimization problem that can be solved using gradient descent given a set of sampled trajectories, making our method suitable for high-dimensional problems with large state spaces. We empirically validate the method, by showing that it can successfully learn a useful hierarchical representation in a navigation domain. Once learned, the hierarchical representation can be used to solve different tasks in the given domain, thus generalizing knowledge across tasks.

The goal of controlled feature selection is to discover the features a response depends on while limiting the proportion of false discoveries to a predefined level. Recently, multiple methods have been proposed that use deep learning to generate knockoffs for controlled feature selection through the Model-X knockoff framework. We demonstrate, however, that these methods often fail to control the false discovery rate (FDR). There are two reasons for this shortcoming. First, these methods often learn inaccurate models of features. Second, the "swap" property, which is required for knockoffs to be valid, is often not well enforced. We propose a new procedure called FlowSelect that remedies both of these problems. To more accurately model the features, FlowSelect uses normalizing flows, the state-of-the-art method for density estimation. To circumvent the need to enforce the swap property, FlowSelect uses a novel MCMC-based procedure to directly compute p-values for each feature. Asymptotically, FlowSelect controls the FDR exactly. Empirically, FlowSelect controls the FDR well on both synthetic and semi-synthetic benchmarks, whereas competing knockoff-based approaches fail to do so. FlowSelect also demonstrates greater power on these benchmarks. Additionally, using data from a genome-wide association study of soybeans, FlowSelect correctly infers the genetic variants associated with specific soybean traits.

This paper presents the first {\em model-free}, {\em simulator-free} reinforcement learning algorithm for Constrained Markov Decision Processes (CMDPs) with sublinear regret and zero constraint violation. The algorithm is named Triple-Q because it has three key components: a Q-function (also called action-value function) for the cumulative reward, a Q-function for the cumulative utility for the constraint, and a virtual-Queue that (over)-estimates the cumulative constraint violation. Under Triple-Q, at each step, an action is chosen based on the pseudo-Q-value that is a combination of the three Q values. The algorithm updates the reward and utility Q-values with learning rates that depend on the visit counts to the corresponding (state, action) pairs and are periodically reset. In the episodic CMDP setting, Triple-Q achieves $\tilde{\cal O}\left(\frac{1 }{\delta}H^4 S^{\frac{1}{2}}A^{\frac{1}{2}}K^{\frac{4}{5}} \right)$ regret, where $K$ is the total number of episodes, $H$ is the number of steps in each episode, $S$ is the number of states, $A$ is the number of actions, and $\delta$ is Slater's constant. Furthermore, Triple-Q guarantees zero constraint violation when $K$ is sufficiently large. Finally, the computational complexity of Triple-Q is similar to SARSA for unconstrained MDPs and is computationally efficient.

Inferring social relations from dialogues is vital for building emotionally intelligent robots to interpret human language better and act accordingly. We model the social network as an And-or Graph, named SocAoG, for the consistency of relations among a group and leveraging attributes as inference cues. Moreover, we formulate a sequential structure prediction task, and propose an $\alpha$-$\beta$-$\gamma$ strategy to incrementally parse SocAoG for the dynamic inference upon any incoming utterance: (i) an $\alpha$ process predicting attributes and relations conditioned on the semantics of dialogues, (ii) a $\beta$ process updating the social relations based on related attributes, and (iii) a $\gamma$ process updating individual's attributes based on interpersonal social relations. Empirical results on DialogRE and MovieGraph show that our model infers social relations more accurately than the state-of-the-art methods. Moreover, the ablation study shows the three processes complement each other, and the case study demonstrates the dynamic relational inference.

Finding different solutions to the same problem is a key aspect of intelligence associated with creativity and adaptation to novel situations. In reinforcement learning, a set of diverse policies can be useful for exploration, transfer, hierarchy, and robustness. We propose Diverse Successive Policies, a method for discovering policies that are diverse in the space of Successor Features, while assuring that they are near optimal. We formalize the problem as a Constrained Markov Decision Process (CMDP) where the goal is to find policies that maximize diversity, characterized by an intrinsic diversity reward, while remaining near-optimal with respect to the extrinsic reward of the MDP. We also analyze how recently proposed robustness and discrimination rewards perform and find that they are sensitive to the initialization of the procedure and may converge to sub-optimal solutions. To alleviate this, we propose new explicit diversity rewards that aim to minimize the correlation between the Successor Features of the policies in the set. We compare the different diversity mechanisms in the DeepMind Control Suite and find that the type of explicit diversity we are proposing is important to discover distinct behavior, like for example different locomotion patterns.

To successfully negotiate a deal, it is not enough to communicate fluently: pragmatic planning of persuasive negotiation strategies is essential. While modern dialogue agents excel at generating fluent sentences, they still lack pragmatic grounding and cannot reason strategically. We present DialoGraph, a negotiation system that incorporates pragmatic strategies in a negotiation dialogue using graph neural networks. DialoGraph explicitly incorporates dependencies between sequences of strategies to enable improved and interpretable prediction of next optimal strategies, given the dialogue context. Our graph-based method outperforms prior state-of-the-art negotiation models both in the accuracy of strategy/dialogue act prediction and in the quality of downstream dialogue response generation. We qualitatively show further benefits of learned strategy-graphs in providing explicit associations between effective negotiation strategies over the course of the dialogue, leading to interpretable and strategic dialogues.