We study the problem of modeling human mobility from semantic trace data, wherein each GPS record in a trace is associated with a text message that describes the user's activity. Existing methods fall short in unveiling human movement regularities, because they either do not model the text data at all or suffer from text sparsity severely. We propose SHMM, a multi-modal spherical hidden Markov model for semantics-rich human mobility modeling. Under the hidden Markov assumption, SHMM models the generation process of a given trace by jointly considering the observed location, time, and text at each step of the trace. The distinguishing characteristic of SHMM is the text modeling part. We use fixed-size vector representations to encode the semantics of the text messages, and model the generation of the l2-normalized text embeddings on a unit sphere with the von Mises-Fisher (vMF) distribution. Compared with other alternatives like multi-variate Gaussian, our choice of the vMF distribution not only incurs much fewer parameters, but also better leverages the discriminative power of text embeddings in a directional metric space. The parameter inference for the vMF distribution is non-trivial since it involves functional inversion of ratios of Bessel functions. We theoretically prove that: 1) the classical Expectation-Maximization algorithm can work with vMF distributions; and 2) while closed-form solutions are hard to be obtained for the M-step, Newton's method is guaranteed to converge to the optimal solution with quadratic convergence rate. We have performed extensive experiments on both synthetic and real-life data. The results on synthetic data verify our theoretical analysis; while the results on real-life data demonstrate that SHMM learns meaningful semantics-rich mobility models, outperforms state-of-the-art mobility models for next location prediction, and incurs lower training cost.

Reinforcement Learning (RL) agents typically learn memoryless policies---policies that only consider the last observation when selecting actions. Learning memoryless policies is efficient and optimal in fully observable environments. However, some form of memory is necessary when RL agents are faced with partial observability. In this paper, we study a lightweight approach to tackle partial observability in RL. We provide the agent with an external memory and additional actions to control what, if anything, is written to the memory. At every step, the current memory state is part of the agent's observation, and the agent selects a tuple of actions: one action that modifies the environment and another that modifies the memory. When the external memory is sufficiently expressive, optimal memoryless policies yield globally optimal solutions. Unfortunately, previous attempts to use external memory in the form of binary memory have produced poor results in practice. Here, we investigate alternative forms of memory in support of learning effective memoryless policies. Our novel forms of memory outperform binary and LSTM-based memory in well-established partially observable domains.

Model-based algorithms---algorithms that decouple learning of the model and planning given the model---are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for single-agent reinforcement learning in Markov Decision Processes (MDPs). However, for multi-agent reinforcement learning in Markov games, the current best known sample complexity for model-based algorithms is rather suboptimal and compares unfavorably against recent model-free approaches. In this paper, we present a sharp analysis of model-based self-play algorithms for multi-agent Markov games. We design an algorithm \emph{Optimistic Nash Value Iteration} (Nash-VI) for two-player zero-sum Markov games that is able to output an $\epsilon$-approximate Nash policy in $\tilde{\mathcal{O}}(H^3SAB/\epsilon^2)$ episodes of game playing, where $S$ is the number of states, $A,B$ are the number of actions for the two players respectively, and $H$ is the horizon length. This is the first algorithm that matches the information-theoretic lower bound $\Omega(H^3S(A+B)/\epsilon^2)$ except for a $\min\{A,B\}$ factor, and compares favorably against the best known model-free algorithm if $\min\{A,B\}=o(H^3)$. In addition, our Nash-VI outputs a single Markov policy with optimality guarantee, while existing sample-efficient model-free algorithms output a nested mixture of Markov policies that is in general non-Markov and rather inconvenient to store and execute. We further adapt our analysis to designing a provably efficient task-agnostic algorithm for zero-sum Markov games, and designing the first line of provably sample-efficient algorithms for multi-player general-sum Markov games.

Langevin Monte Carlo (LMC) is a popular Markov chain Monte Carlo sampling method. One drawback is that it requires the computation of the full gradient at each iteration, an expensive operation if the dimension of the problem is high. We propose a new sampling method: Random Coordinate LMC (RC-LMC). At each iteration, a single coordinate is randomly selected to be updated by a multiple of the partial derivative along this direction plus noise, and all other coordinates remain untouched. We investigate the total complexity of RC-LMC and compare it with the classical LMC for log-concave probability distributions. When the gradient of the log-density is Lipschitz, RC-LMC is less expensive than the classical LMC if the log-density is highly skewed for high dimensional problems, and when both the gradient and the Hessian of the log-density are Lipschitz, RC-LMC is always cheaper than the classical LMC, by a factor proportional to the square root of the problem dimension. In the latter case, our estimate of complexity is sharp with respect to the dimension.

Reinforcement learning (RL) and planning in Markov decision processes (MDPs) is one type of dynamic decisionmaking problem (Puterman, 1994; Bertsekas & Tsitsiklis, 1996; sut, 1998). While the typical objective is to maximize the expected cumulative reward, risk-aware decision-making has attracted attention in real-world applications, such as finance, robotics, and playing games (Geibel & Wysotzki, 2005; García & Fernández, 2015). The notion of risk in RL is related to the fact that even an optimal policy may perform poorly in some cases owing to the stochastic nature of the problem. To capture the risk, various criteria have been proposed, such as Value at Risk (Luenberger, 1998; Chow & Ghavamzadeh, 2014; Chow et al., 2017) and variance (Markowitz, 1952; Markowitz et al., 2000; Tamar et al., 2012; L.A. & Ghavamzadeh, 2013). Among them, we focus on the mean-variance tradeoff in RL problems. Typical mean-variance RL (MVRL) methods attempt to maximize the expected cumulative reward while maintaining the variance threshold (Tamar et al., 2012; L.A. & Ghavamzadeh, 2013; Prashanth & Ghavamzadeh, 2016; Xie et al., 2018; Bisi et al., 2020; Zhang et al., 2020). However, most existing MVRL methods suffer from high computational costs owing to the double sampling issue when approximating the gradient of the variance term (Tamar et al., 2012; L.A. & Ghavamzadeh, 2013; Prashanth & Ghavamzadeh, 2016). To avoid the double sampling issue, Xie et al. (2018) proposed a method based on the Legendre-Fenchel duality (Boyd & Vandenberghe, 2004). Although the method does not suffer from the double sampling issue, we cannot apply a standard policy gradient method and must use a coordinate descent algorithm.

End-to-end task-oriented dialogue systems aim to generate system responses directly from plain text inputs. There are two challenges for such systems: one is how to effectively incorporate external knowledge bases (KBs) into the learning framework; the other is how to accurately capture the semantics of dialogue history. In this paper, we address these two challenges by exploiting the graph structural information in the knowledge base and in the dependency parsing tree of the dialogue. To effectively leverage the structural information in dialogue history, we propose a new recurrent cell architecture which allows representation learning on graphs. To exploit the relations between entities in KBs, the model combines multi-hop reasoning ability based on the graph structure. Experimental results show that the proposed model achieves consistent improvement over state-of-the-art models on two different task-oriented dialogue datasets.

We consider the problem of local planning in fixed-horizon Markov Decision Processes (MDPs) with linear function approximation and a generative model under the assumption that the optimal action-value function lies in the span of a feature map that is available to the planner. Previous work has left open the question of whether there exists sound planners that need only poly(H, d) queries regardless of the MDP, where H is the horizon and d is the dimensionality of the features. We answer this question in the negative: we show that any sound planner must query at least min(exp({\Omega}(d)), {\Omega}(2^H)) samples. We also show that for any {\delta}>0, the least-squares value iteration algorithm with O(H^5d^(H+1)/{\delta}^2) queries can compute a {\delta}-optimal policy. We discuss implications and remaining open questions.

Model-based reinforcement learning (MBRL) has been applied to meta-learning settings and has demonstrated its high sample efficiency. However, in previous MBRL for meta-learning settings, policies are optimized via rollouts that fully rely on a predictive model of an environment. Thus, its performance in a real environment tends to degrade when the predictive model is inaccurate. In this paper, we prove that performance degradation can be suppressed by using branched meta-rollouts. On the basis of this theoretical analysis, we propose Meta-Model-based Meta-Policy Optimization (M3PO), in which the branched meta-rollouts are used for policy optimization. We demonstrate that M3PO outperforms existing meta reinforcement learning methods in continuous-control benchmarks.

This work demonstrates how a complete statistical model quantifying the evolution of pairs of aligned proteins can be constructed from a time-parameterised substitution matrix and a time-parameterised 3-state alignment machine. All parameters of such a model can be inferred from any benchmark data-set of aligned protein sequences. This allows us to examine nine well-known substitution matrices on six benchmarks curated using various structural alignment methods; any matrix that does not explicitly model a "time"-dependent Markov process is converted to a corresponding base-matrix that does. In addition, a new optimal matrix is inferred for each of the six benchmarks. Using Minimum Message Length (MML) inference, all 15 matrices are compared in terms of measuring the Shannon information content of each benchmark. This has resulted in a new and clear overall best performed time-dependent Markov matrix, MMLSUM, and its associated 3-state machine, whose properties we have analysed in this work. For standard use, the MMLSUM series of (log-odds) \textit{scoring} matrices derived from the above Markov matrix, are available at https://lcb.infotech.monash.edu.au/mmlsum.

The most common representation formalisms for automated planning are descriptive models that abstractly describe what the actions do and are tailored for effciently computing the next state(s) in a state-transition system. However, real-world acting requires operational models that describe how to do things, with rich control structures for closed-loop online decision-making in a dynamic environment. To use a different action model for planning than the one used for acting causes problems with combining acting and planning, in particular for the development and consistency verification of the different models. As an alternative, we define and implement an integrated acting-and-planning system in which both planning and acting use the same operational models, which are written in a general-purpose hierarchical task-oriented language offering rich control structures. The acting component, called Reactive Acting Engine (RAE), is inspired by the well-known PRS system, except that instead of being purely reactive, it can get advice from the planner. Our planner uses a UCT-like Monte Carlo Tree Search procedure, called UPOM (UCT Procedure for Operational Models), whose rollouts are simulations of the actor's operational models. We also present learning strategies for use with RAE and UPOM that acquire, from online acting experiences and/or simulated planning results, a mapping from decision contexts to method instances as well as a heuristic function to guide UPOM. Our experimental results show that UPOM and our learning strategies significantly improve the acting efficiency and robustness of RAE. We discuss the asymptotic convergence of UPOM by mapping its search space to an MDP.