A long-standing challenge in artificial intelligence is lifelong learning. In lifelong learning, many tasks are presented in sequence and learners must efficiently transfer knowledge between tasks while avoiding catastrophic forgetting over long lifetimes. On these problems, policy reuse and other multi-policy reinforcement learning techniques can learn many tasks. However, they can generate many temporary or permanent policies, resulting in memory issues. Consequently, there is a need for lifetime-scalable methods that continually refine a policy library of a pre-defined size. This paper presents a first approach to lifetime-scalable policy reuse. To pre-select the number of policies, a notion of task capacity, the maximal number of tasks that a policy can accurately solve, is proposed. To evaluate lifetime policy reuse using this method, two state-of-the-art single-actor base-learners are compared: 1) a value-based reinforcement learner, Deep Q-Network (DQN) or Deep Recurrent Q-Network (DRQN); and 2) an actor-critic reinforcement learner, Proximal Policy Optimisation (PPO) with or without Long Short-Term Memory layer. By selecting the number of policies based on task capacity, D(R)QN achieves near-optimal performance with 6 policies in a 27-task MDP domain and 9 policies in an 18-task POMDP domain; with fewer policies, catastrophic forgetting and negative transfer are observed. Due to slow, monotonic improvement, PPO requires fewer policies, 1 policy for the 27-task domain and 4 policies for the 18-task domain, but it learns the tasks with lower accuracy than D(R)QN. These findings validate lifetime-scalable policy reuse and suggest using D(R)QN for larger and PPO for smaller library sizes. During their lifetime, animals may be subjected to a large number of unknown tasks. In some environmental conditions, nutritious food sources may be readily available, while in others they may be sparse, hidden, or even poisonous, and dangerous predators may roam in their vicinity. To address these challenging conditions, various behaviours must be selectively combined, such as avoidance, reward-seeking, or even fleeing. When direct perception provides limited or no cues about the current task, animals have to infer the task or use a strategy that works for many different tasks it may encounter. Therefore, a key challenge for learning challenging sequences of tasks is to find a limited number of strategies that work on the large domain of tasks that animals encounter over their lifetime. In artificial intelligence, variants of the above problem have been studied with investigations focusing on two aspects: transfer learning and catastrophic forgetting. Transfer learning is a process in which learners leverage the knowledge gained from a set of previously learned tasks with similar characteristics to a new task, whilst avoiding transferring knowledge that is not relevant [Taylor and Stone, 2009, Pan and Yang, 2010, Lazaric, 2013].

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be unfeasible. We propose a new class of methods to overcome these challenges in the common case of sparse constraints, where one has a large number of constraints and each only involves a few elements. Our methods rely on a basis transformation into blocks of constrained versus non-constrained subspaces, and we show that the methods greatly outperform existing alternatives in terms of computational cost. By combining the proposed methods with the stochastic partial differential equation approach for Gaussian random fields, we also show how to formulate Gaussian process regression with linear constraints in a GMRF setting to reduce computational cost. This is illustrated in two applications with simulated data.

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.