Generalization in reinforcement learning (RL) is of importance for real deployment of RL algorithms. Various schemes are proposed to address the generalization issues, including transfer learning, multi-task learning and meta learning, as well as the robust and adversarial reinforcement learning. However, there is not a unified formulation of the various schemes, as well as the comprehensive comparisons of methods across different schemes. In this work, we propose a game-theoretic framework for the generalization in reinforcement learning, named GiRL, where an RL agent is trained against an adversary over a set of tasks, where the adversary can manipulate the distributions over tasks within a given threshold. With different configurations, GiRL can reduce the various schemes mentioned above. To solve GiRL, we adapt the widely-used method in game theory, policy space response oracle (PSRO) with the following three important modifications: i) we use model-agnostic meta learning (MAML) as the best-response oracle, ii) we propose a modified projected replicated dynamics, i.e., R-PRD, which ensures the computed meta-strategy of the adversary fall in the threshold, and iii) we also propose a protocol for the few-shot learning of the multiple strategies during testing. Extensive experiments on MuJoCo environments demonstrate that our proposed methods can outperform existing baselines, e.g., MAML.

Deep reinforcement learning (RL) has achieved significant progress in recent years with particular success in games (Mnih et al., 2015, Silver et al., 2016, Vinyals et al., 2019). RL methods applied to the setting where a reward is only given at the end (i.e., terminal states) typically aim at maximizing that reward function for learning the optimal policy. However, diversity of the generated states is desirable in a wide range of practical scenarios including molecule generation (Bengio et al., 2021a), biological sequence design (Jain et al., 2022b), recommender systems (Kunaver and Požrl, 2017), dialogue systems (Zhang et al., 2020), etc. For example, in molecule generation, the reward function used in in-silico simulations can be uncertain and imperfect itself (compared to the more expensive in-vivo experiments). Therefore, it is not sufficient to only search the solution that maximizes the return. Instead, it is desired that we sample many high-reward candidates, which can be achieved by sampling them proportionally to the reward of each terminal state. Interestingly, GFlowNets (Bengio et al., 2021a,b) learn a stochastic policy to sample composite objects x X with probability proportional to the return R(x) . The learning paradigm of GFlowNets is different from other RL methods, as it is explicitly aiming at modeling the diversity in the target distribution, i.e., all the modes of the reward function. This makes it natural for practical applications where the model should discover objects that are both interesting and diverse, which is a focus of previous GFlowNet works (Bengio et al., 2021a,b, Jain et al., 2022b, Malkin et al., 2022).

Applying Reinforcement learning (RL) following maximum likelihood estimation (MLE) pre-training is a versatile method for enhancing neural machine translation (NMT) performance. However, recent work has argued that the gains produced by RL for NMT are mostly due to promoting tokens that have already received a fairly high probability in pre-training. We hypothesize that the large action space is a main obstacle to RL's effectiveness in MT, and conduct two sets of experiments that lend support to our hypothesis. First, we find that reducing the size of the vocabulary improves RL's effectiveness. Second, we find that effectively reducing the dimension of the action space without changing the vocabulary also yields notable improvement as evaluated by BLEU, semantic similarity, and human evaluation. Indeed, by initializing the network's final fully connected layer (that maps the network's internal dimension to the vocabulary dimension), with a layer that generalizes over similar actions, we obtain a substantial improvement in RL performance: 1.5 BLEU points on average.

Purpose: Real-life applications using quadrotors introduce a number of disturbances and time-varying properties that pose a challenge to flight controllers. We observed that, when a quadrotor is tasked with picking up and dropping a payload, traditional PID and RL-based controllers found in literature struggle to maintain flight after the vehicle changes its dynamics due to interaction with this external object. Methods: In this work, we introduce domain randomization during the training phase of a low-level waypoint guidance controller based on Soft Actor-Critic. The resulting controller is evaluated on the proposed payload pick up and drop task with added disturbances that emulate real-life operation of the vehicle. Results & Conclusion: We show that, by introducing a certain degree of uncertainty in quadrotor dynamics during training, we can obtain a controller that is capable to perform the proposed task using a larger variation of quadrotor parameters. Additionally, the RL-based controller outperforms a traditional positional PID controller with optimized gains in this task, while remaining agnostic to different simulation parameters.

The process of robot design is a complex task and the majority of design decisions are still based on human intuition or tedious manual tuning. A more informed way of facing this task is computational design methods where design parameters are concurrently optimized with corresponding controllers. Existing approaches, however, are strongly influenced by predefined control rules or motion templates and cannot provide end-to-end solutions. In this paper, we present a design optimization framework using model-free meta reinforcement learning, and its application to the optimizing kinematics and actuator parameters of quadrupedal robots. We use meta reinforcement learning to train a locomotion policy that can quickly adapt to different designs. This policy is used to evaluate each design instance during the design optimization. We demonstrate that the policy can control robots of different designs to track random velocity commands over various rough terrains. With controlled experiments, we show that the meta policy achieves close-to-optimal performance for each design instance after adaptation. Lastly, we compare our results against a model-based baseline and show that our approach allows higher performance while not being constrained by predefined motions or gait patterns.

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions and large datasets. We address the bottleneck problem arising when using both shared and distributed memory. Typically, the former is bounded by limited computation resources and bandwidth whereas the latter suffers from communication overheads. We propose a unified distributed and parallel implementation of SGD (named DPSGD) that relies on both asynchronous distribution and lock-free parallelism. By combining two strategies into a unified framework, DPSGD is able to strike a better trade-off between local computation and communication. The convergence properties of DPSGD are studied for non-convex problems such as those arising in statistical modelling and machine learning. Our theoretical analysis shows that DPSGD leads to speed-up with respect to the number of cores and number of workers while guaranteeing an asymptotic convergence rate of $O(1/\sqrt{T})$ given that the number of cores is bounded by $T^{1/4}$ and the number of workers is bounded by $T^{1/2}$ where $T$ is the number of iterations. The potential gains that can be achieved by DPSGD are demonstrated empirically on a stochastic variational inference problem (Latent Dirichlet Allocation) and on a deep reinforcement learning (DRL) problem (advantage actor critic - A2C) resulting in two algorithms: DPSVI and HSA2C. Empirical results validate our theoretical findings. Comparative studies are conducted to show the performance of the proposed DPSGD against the state-of-the-art DRL algorithms.

Improving the efficiency of algorithms for fundamental computations can have a widespread impact, as it can affect the overall speed of a large amount of computations. Matrix multiplication is one such primitive task, occurring in many systems—from neural networks to scientific computing routines. The automatic discovery of algorithms using machine learning offers the prospect of reaching beyond human intuition and outperforming the current best human-designed algorithms. However, automating the algorithm discovery procedure is intricate, as the space of possible algorithms is enormous. Here we report a deep reinforcement learning approach based on AlphaZero1 for discovering efficient and provably correct algorithms for the multiplication of arbitrary matrices. Our agent, AlphaTensor, is trained to play a single-player game where the objective is finding tensor decompositions within a finite factor space. AlphaTensor discovered algorithms that outperform the state-of-the-art complexity for many matrix sizes. Particularly relevant is the case of 4 × 4 matrices in a finite field, where AlphaTensor’s algorithm improves on Strassen’s two-level algorithm for the first time, to our knowledge, since its discovery 50 years ago2. We further showcase the flexibility of AlphaTensor through different use-cases: algorithms with state-of-the-art complexity for structured matrix multiplication and improved practical efficiency by optimizing matrix multiplication for runtime on specific hardware. Our results highlight AlphaTensor’s ability to accelerate the process of algorithmic discovery on a range of problems, and to optimize for different criteria. A reinforcement learning approach based on AlphaZero is used to discover efficient and provably correct algorithms for matrix multiplication, finding faster algorithms for a variety of matrix sizes.

In this thesis, we research learning algorithms for optimal decision making in two different contexts, Reinforcement Learning in Part I and Auction Design in Part II. Reinforcement learning (RL) is an area of machine learning that is concerned with how an agent should act in an environment in order to maximize its cumulative reward over time. In Chapter 2, inspired by statistical physics, we develop a novel approach to Reinforcement Learning (RL) that not only learns optimal policies with enhanced desirable properties but also sheds new light on maximum entropy RL. In Chapter 3, we tackle the generalization problem in RL using a Bayesian perspective. We show that imperfect knowledge of the environments dynamics effectively turn a fully-observed Markov Decision Process (MDP) into a Partially Observed MDP (POMDP) that we call the Epistemic POMDP. Informed by this observation, we develop a new policy learning algorithm LEEP which has improved generalization properties. Designing an incentive compatible, individually rational auction that maximizes revenue is a challenging and intractable problem. Recently, deep learning based approaches have been proposed to learn optimal auctions from data. While successful, this approach suffers from a few limitations, including sample inefficiency, lack of generalization to new auctions, and training difficulties. In Chapter 4, we construct a symmetry preserving neural network architecture, EquivariantNet, suitable for anonymous auctions. EquivariantNet is not only more sample efficient but is also able to learn auction rules that generalize well to other settings. In Chapter 5, we propose a novel formulation of the auction learning problem as a two player game. The resulting learning algorithm, ALGNet, is easier to train, more reliable and better suited for non stationary settings.

We study the problem of episodic reinforcement learning in continuous state-action spaces with unknown rewards and transitions. Specifically, we consider the setting where the rewards and transitions are modeled using parametric bilinear exponential families. We propose an algorithm, BEF-RLSVI, that a) uses penalized maximum likelihood estimators to learn the unknown parameters, b) injects a calibrated Gaussian noise in the parameter of rewards to ensure exploration, and c) leverages linearity of the exponential family with respect to an underlying RKHS to perform tractable planning. We further provide a frequentist regret analysis of BEF-RLSVI that yields an upper bound of $\tilde{\mathcal{O}}(\sqrt{d^3H^3K})$, where $d$ is the dimension of the parameters, $H$ is the episode length, and $K$ is the number of episodes. Our analysis improves the existing bounds for the bilinear exponential family of MDPs by $\sqrt{H}$ and removes the handcrafted clipping deployed in existing \RLSVI-type algorithms. Our regret bound is order-optimal with respect to $H$ and $K$.

Although transfer learning is considered to be a milestone in deep reinforcement learning, the mechanisms behind it are still poorly understood. In particular, predicting if knowledge can be transferred between two given tasks is still an unresolved problem. In this work, we explore the use of network distillation as a feature extraction method to better understand the context in which transfer can occur. Notably, we show that distillation does not prevent knowledge transfer, including when transferring from multiple tasks to a new one, and we compare these results with transfer without prior distillation. We focus our work on the Atari benchmark due to the variability between different games, but also to their similarities in terms of visual features.