Successful applications of distributional reinforcement learning with quantile regression prompt a natural question: can we use other statistics to represent the distribution of returns? In particular, expectile regression is known to be more efficient than quantile regression for approximating distributions, especially on extreme values, and by providing a straightforward estimator of the mean it is a natural candidate for reinforcement learning. Prior work has answered this question positively in the case of expectiles, with the major caveat that expensive computations must be performed to ensure convergence. In this work, we propose a dual expectile-quantile approach which solves the shortcomings of previous work while leveraging the complementary properties of expectiles and quantiles. Our method outperforms both quantile-based and expectile-based baselines on the MuJoCo continuous control benchmark.
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It is well known that it is impossible to construct useful confidence intervals (CIs) about the mean or median of a response $Y$ conditional on features $X = x$ without making strong assumptions about the joint distribution of $X$ and $Y$. This paper introduces a new framework for reasoning about problems of this kind by casting the conditional problem at different levels of resolution, ranging from coarse to fine localization. In each of these problems, we consider local quantiles defined as the marginal quantiles of $Y$ when $(X,Y)$ is resampled in such a way that samples $X$ near $x$ are up-weighted while the conditional distribution $Y \mid X$ does not change. We then introduce the Weighted Quantile method, which asymptotically produces the uniformly most accurate confidence intervals for these local quantiles no matter the (unknown) underlying distribution. Another method, namely, the Quantile Rejection method, achieves finite sample validity under no assumption whatsoever. We conduct extensive numerical studies demonstrating that both of these methods are valid. In particular, we show that the Weighted Quantile procedure achieves nominal coverage as soon as the effective sample size is in the range of 10 to 20.
Time-to-event analysis, also known as survival analysis, aims to predict the time of occurrence of an event, given a set of features. One of the major challenges in this area is dealing with censored data, which can make learning algorithms more complex. Traditional methods such as Cox's proportional hazards model and the accelerated failure time (AFT) model have been popular in this field, but they often require assumptions such as proportional hazards and linearity. In particular, the AFT models often require pre-specified parametric distributional assumptions. To improve predictive performance and alleviate strict assumptions, there have been many deep learning approaches for hazard-based models in recent years. However, representation learning for AFT has not been widely explored in the neural network literature, despite its simplicity and interpretability in comparison to hazard-focused methods. In this work, we introduce the Deep AFT Rank-regression model for Time-to-event prediction (DART). This model uses an objective function based on Gehan's rank statistic, which is efficient and reliable for representation learning. On top of eliminating the requirement to establish a baseline event time distribution, DART retains the advantages of directly predicting event time in standard AFT models. The proposed method is a semiparametric approach to AFT modeling that does not impose any distributional assumptions on the survival time distribution. This also eliminates the need for additional hyperparameters or complex model architectures, unlike existing neural network-based AFT models. Through quantitative analysis on various benchmark datasets, we have shown that DART has significant potential for modeling high-throughput censored time-to-event data.
We evaluate benchmark deep reinforcement learning (DRL) algorithms on the task of portfolio optimisation under a simulator. The simulator is based on correlated geometric Brownian motion (GBM) with the Bertsimas-Lo (BL) market impact model. Using the Kelly criterion (log utility) as the objective, we can analytically derive the optimal policy without market impact and use it as an upper bound to measure performance when including market impact. We found that the off-policy algorithms DDPG, TD3 and SAC were unable to learn the right Q function due to the noisy rewards and therefore perform poorly. The on-policy algorithms PPO and A2C, with the use of generalised advantage estimation (GAE), were able to deal with the noise and derive a close to optimal policy. The clipping variant of PPO was found to be important in preventing the policy from deviating from the optimal once converged. In a more challenging environment where we have regime changes in the GBM parameters, we found that PPO, combined with a hidden Markov model (HMM) to learn and predict the regime context, is able to learn different policies adapted to each regime. Overall, we find that the sample complexity of these algorithms is too high, requiring more than 2m steps to learn a good policy in the simplest setting, which is equivalent to almost 8,000 years of daily prices.
By incorporating regret minimization, double oracle methods have demonstrated rapid convergence to Nash Equilibrium (NE) in normal-form games and extensive-form games, through algorithms such as online double oracle (ODO) and extensive-form double oracle (XDO), respectively. In this study, we further examine the theoretical convergence rate and sample complexity of such regret minimization-based double oracle methods, utilizing a unified framework called Regret-Minimizing Double Oracle. Based on this framework, we extend ODO to extensive-form games and determine its sample complexity. Moreover, we demonstrate that the sample complexity of XDO can be exponential in the number of information sets $|S|$, owing to the exponentially decaying stopping threshold of restricted games. To solve this problem, we propose the Periodic Double Oracle (PDO) method, which has the lowest sample complexity among regret minimization-based double oracle methods, being only polynomial in $|S|$. Empirical evaluations on multiple poker and board games show that PDO achieves significantly faster convergence than previous double oracle algorithms and reaches a competitive level with state-of-the-art regret minimization methods.
Bayesian policy reuse (BPR) is a general policy transfer framework for selecting a source policy from an offline library by inferring the task belief based on some observation signals and a trained observation model. In this paper, we propose an improved BPR method to achieve more efficient policy transfer in deep reinforcement learning (DRL). First, most BPR algorithms use the episodic return as the observation signal that contains limited information and cannot be obtained until the end of an episode. Instead, we employ the state transition sample, which is informative and instantaneous, as the observation signal for faster and more accurate task inference. Second, BPR algorithms usually require numerous samples to estimate the probability distribution of the tabular-based observation model, which may be expensive and even infeasible to learn and maintain, especially when using the state transition sample as the signal. Hence, we propose a scalable observation model based on fitting state transition functions of source tasks from only a small number of samples, which can generalize to any signals observed in the target task. Moreover, we extend the offline-mode BPR to the continual learning setting by expanding the scalable observation model in a plug-and-play fashion, which can avoid negative transfer when faced with new unknown tasks. Experimental results show that our method can consistently facilitate faster and more efficient policy transfer.
Inverse reinforcement learning (IRL) algorithms often rely on (forward) reinforcement learning or planning over a given time horizon to compute an approximately optimal policy for a hypothesized reward function and then match this policy with expert demonstrations. The time horizon plays a critical role in determining both the accuracy of reward estimate and the computational efficiency of IRL algorithms. Interestingly, an effective time horizon shorter than the ground-truth value often produces better results faster. This work formally analyzes this phenomenon and provides an explanation: the time horizon controls the complexity of an induced policy class and mitigates overfitting with limited data. This analysis leads to a principled choice of the effective horizon for IRL. It also prompts us to reexamine the classic IRL formulation: it is more natural to learn jointly the reward and the effective horizon together rather than the reward alone with a given horizon. Our experimental results confirm the theoretical analysis.
The role of cryptocurrencies within the financial systems has been expanding rapidly in recent years among investors and institutions. It is therefore crucial to investigate the phenomena and develop statistical methods able to capture their interrelationships, the links with other global systems, and, at the same time, the serial heterogeneity. For these reasons, this paper introduces hidden Markov regression models for jointly estimating quantiles and expectiles of cryptocurrency returns using regime-switching copulas. The proposed approach allows us to focus on extreme returns and describe their temporal evolution by introducing time-dependent coefficients evolving according to a latent Markov chain. Moreover to model their time-varying dependence structure, we consider elliptical copula functions defined by state-specific parameters. Maximum likelihood estimates are obtained via an Expectation-Maximization algorithm. The empirical analysis investigates the relationship between daily returns of five cryptocurrencies and major world market indices.
The past few years have seen rapid progress in combining reinforcement learning (RL) with deep learning. Various breakthroughs ranging from games to robotics have spurred the interest in designing sophisticated RL algorithms and systems. However, the prevailing workflow in RL is to learn tabula rasa, which may incur computational inefficiency. This precludes continuous deployment of RL algorithms and potentially excludes researchers without large-scale computing resources. In many other areas of machine learning, the pretraining paradigm has shown to be effective in acquiring transferable knowledge, which can be utilized for a variety of downstream tasks. Recently, we saw a surge of interest in Pretraining for Deep RL with promising results. However, much of the research has been based on different experimental settings. Due to the nature of RL, pretraining in this field is faced with unique challenges and hence requires new design principles. In this survey, we seek to systematically review existing works in pretraining for deep reinforcement learning, provide a taxonomy of these methods, discuss each sub-field, and bring attention to open problems and future directions.
The development of autonomous agents which can interact with other agents to accomplish a given task is a core area of research in artificial intelligence and machine learning. Towards this goal, the Autonomous Agents Research Group develops novel machine learning algorithms for autonomous systems control, with a specific focus on deep reinforcement learning and multi-agent reinforcement learning. Research problems include scalable learning of coordinated agent policies and inter-agent communication; reasoning about the behaviours, goals, and composition of other agents from limited observations; and sample-efficient learning based on intrinsic motivation, curriculum learning, causal inference, and representation learning. This article provides a broad overview of the ongoing research portfolio of the group and discusses open problems for future directions.
Advances in artificial intelligence often stem from the development of new environments that abstract real-world situations into a form where research can be done conveniently. This paper contributes such an environment based on ideas inspired by elementary Microeconomics. Agents learn to produce resources in a spatially complex world, trade them with one another, and consume those that they prefer. We show that the emergent production, consumption, and pricing behaviors respond to environmental conditions in the directions predicted by supply and demand shifts in Microeconomics. We also demonstrate settings where the agents' emergent prices for goods vary over space, reflecting the local abundance of goods. After the price disparities emerge, some agents then discover a niche of transporting goods between regions with different prevailing prices -- a profitable strategy because they can buy goods where they are cheap and sell them where they are expensive. Finally, in a series of ablation experiments, we investigate how choices in the environmental rewards, bartering actions, agent architecture, and ability to consume tradable goods can either aid or inhibit the emergence of this economic behavior. This work is part of the environment development branch of a research program that aims to build human-like artificial general intelligence through multi-agent interactions in simulated societies. By exploring which environment features are needed for the basic phenomena of elementary microeconomics to emerge automatically from learning, we arrive at an environment that differs from those studied in prior multi-agent reinforcement learning work along several dimensions. For example, the model incorporates heterogeneous tastes and physical abilities, and agents negotiate with one another as a grounded form of communication.
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