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In recent years, by leveraging more data, computation, and diverse tasks, learned optimizers have achieved remarkable success in supervised learning optimization, outperforming classical hand-designed optimizers. However, in practice, these learned optimizers fail to generalize to reinforcement learning tasks due to unstable and complex loss landscapes. Moreover, neither hand-designed optimizers nor learned optimizers have been specifically designed to address the unique optimization properties in reinforcement learning. In this work, we take a data-driven approach to learn to optimize for reinforcement learning using meta-learning. We introduce a novel optimizer structure that significantly improves the training efficiency of learned optimizers, making it possible to learn an optimizer for reinforcement learning from scratch. Although trained in toy tasks, our learned optimizer demonstrates its generalization ability to unseen complex tasks. Finally, we design a set of small gridworlds to train the first general-purpose optimizer for reinforcement learning.

We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage action from a feasible set that depends both on the first-stage decision and the model parameter. We aim to minimize the cumulative objective value while guaranteeing that the long-term average second-stage decision belongs to a set. We propose a general algorithmic framework that derives online algorithms for the online two-stage problem from adversarial learning algorithms. Also, the regret bound of our algorithm cam be reduced to the regret bound of embedded adversarial learning algorithms. Based on our framework, we obtain new results under various settings. When the model parameter at each period is drawn from identical distributions, we derive state-of-art regret bound that improves previous bounds under special cases. Our algorithm is also robust to adversarial corruptions of model parameter realizations. When the model parameters are drawn from unknown non-stationary distributions and we are given prior estimates of the distributions, we develop a new algorithm from our framework with a regret $O(W_T+\sqrt{T})$, where $W_T$ measures the total inaccuracy of the prior estimates.

Many real-world systems can be described by mathematical formulas that are human-comprehensible, easy to analyze and can be helpful in explaining the system's behaviour. Symbolic regression is a method that generates nonlinear models from data in the form of analytic expressions. Historically, symbolic regression has been predominantly realized using genetic programming, a method that iteratively evolves a population of candidate solutions that are sampled by genetic operators crossover and mutation. This gradient-free evolutionary approach suffers from several deficiencies: it does not scale well with the number of variables and samples in the training data, models tend to grow in size and complexity without an adequate accuracy gain, and it is hard to fine-tune the inner model coefficients using just genetic operators. Recently, neural networks have been applied to learn the whole analytic formula, i.e., its structure as well as the coefficients, by means of gradient-based optimization algorithms. We propose a novel neural network-based symbolic regression method that constructs physically plausible models based on limited training data and prior knowledge about the system. The method employs an adaptive weighting scheme to effectively deal with multiple loss function terms and an epoch-wise learning process to reduce the chance of getting stuck in poor local optima. Furthermore, we propose a parameter-free method for choosing the model with the best interpolation and extrapolation performance out of all models generated through the whole learning process. We experimentally evaluate the approach on the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the anti-lock braking system. The results clearly show the potential of the method to find sparse and accurate models that comply with the prior knowledge provided.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to exploit the temporal dependence of non-conformity scores (e.g., prediction residuals); thus, the past residuals contain information about future ones. Then we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of \texttt{SPCI} compared to other existing methods under the desired empirical coverage.

Computational chemistry has become an important tool to predict and understand molecular properties and reactions. Even though recent years have seen a significant growth in new algorithms and computational methods that speed up quantum chemical calculations, the bottleneck for trajectory-based methods to study photoinduced processes is still the huge number of electronic structure calculations. In this work, we present an innovative solution, in which the amount of electronic structure calculations is drastically reduced, by employing machine learning algorithms and methods borrowed from the realm of artificial intelligence. However, applying these algorithms effectively requires finding optimal hyperparameters, which remains a challenge itself. Here we present an automated user-friendly framework, HOAX, to perform the hyperparameter optimization for neural networks, which bypasses the need for a lengthy manual process. The neural network generated potential energy surfaces (PESs) reduces the computational costs compared to the ab initio-based PESs. We perform a comparative investigation on the performance of different hyperparameter optimiziation algorithms, namely grid search, simulated annealing, genetic algorithm, and bayesian optimizer in finding the optimal hyperparameters necessary for constructing the well-performing neural network in order to fit the PESs of small organic molecules. Our results show that this automated toolkit not only facilitate a straightforward way to perform the hyperparameter optimization but also the resulting neural networks-based generated PESs are in reasonable agreement with the ab initio-based PESs.

Predictive models -- as with machine learning -- can underpin causal inference, to estimate the effects of an intervention at the population or individual level. This opens the door to a plethora of models, useful to match the increasing complexity of health data, but also the Pandora box of model selection: which of these models yield the most valid causal estimates? Classic machine-learning cross-validation procedures are not directly applicable. Indeed, an appropriate selection procedure for causal inference should equally weight both outcome errors for each individual, treated or not treated, whereas one outcome may be seldom observed for a sub-population. We study how more elaborate risks benefit causal model selection. We show theoretically that simple risks are brittle to weak overlap between treated and non-treated individuals as well as to heterogeneous errors between populations. Rather a more elaborate metric, the R-risk appears as a proxy of the oracle error on causal estimates, observable at the cost of an overlap re-weighting. As the R-risk is defined not only from model predictions but also by using the conditional mean outcome and the treatment probability, using it for model selection requires adapting cross validation. Extensive experiments show that the resulting procedure gives the best causal model selection.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting $\textit{Internally Rewarded Reinforcement Learning}$ (IRRL) as the reward is not provided directly by the environment but $\textit{internally}$ by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

Various methods for Multi-Agent Reinforcement Learning (MARL) have been developed with the assumption that agents' policies are based on accurate state information. However, policies learned through Deep Reinforcement Learning (DRL) are susceptible to adversarial state perturbation attacks. In this work, we propose a State-Adversarial Markov Game (SAMG) and make the first attempt to investigate the fundamental properties of MARL under state uncertainties. Our analysis shows that the commonly used solution concepts of optimal agent policy and robust Nash equilibrium do not always exist in SAMGs. To circumvent this difficulty, we consider a new solution concept called robust agent policy, where agents aim to maximize the worst-case expected state value. We prove the existence of robust agent policy for finite state and finite action SAMGs. Additionally, we propose a Robust Multi-Agent Adversarial Actor-Critic (RMA3C) algorithm to learn robust policies for MARL agents under state uncertainties. Our experiments demonstrate that our algorithm outperforms existing methods when faced with state perturbations and greatly improves the robustness of MARL policies. Our code is public on //songyanghan.github.io/what_is_solution/.

Offline model selection (OMS), that is, choosing the best policy from a set of many policies given only logged data, is crucial for applying offline RL in real-world settings. One idea that has been extensively explored is to select policies based on the mean squared Bellman error (MSBE) of the associated Q-functions. However, previous work has struggled to obtain adequate OMS performance with Bellman errors, leading many researchers to abandon the idea. Through theoretical and empirical analyses, we elucidate why previous work has seen pessimistic results with Bellman errors and identify conditions under which OMS algorithms based on Bellman errors will perform well. Moreover, we develop a new estimator of the MSBE that is more accurate than prior methods and obtains impressive OMS performance on diverse discrete control tasks, including Atari games. We open-source our data and code to enable researchers to conduct OMS experiments more easily.

This effort is focused on examining the behavior of reinforcement learning systems in personalization environments and detailing the differences in policy entropy associated with the type of learning algorithm utilized. We demonstrate that Policy Optimization agents often possess low-entropy policies during training, which in practice results in agents prioritizing certain actions and avoiding others. Conversely, we also show that Q-Learning agents are far less susceptible to such behavior and generally maintain high-entropy policies throughout training, which is often preferable in real-world applications. We provide a wide range of numerical experiments as well as theoretical justification to show that these differences in entropy are due to the type of learning being employed.