Cross Entropy versus Label Smoothing: A Neural Collapse Perspective

Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC), a powerful empirical and theoretical framework which characterizes model behavior during the terminal phase of training. We first show empirically that models trained with label smoothing converge faster to neural collapse solutions and attain a stronger level of neural collapse. Additionally, we show that at the same level of NC1, models under label smoothing loss exhibit intensified NC2. These findings provide valuable insights into the performance benefits and enhanced model calibration under label smoothing loss. We then leverage the unconstrained feature model to derive closed-form solutions for the global minimizers for both loss functions and further demonstrate that models under label smoothing have a lower conditioning number and, therefore, theoretically converge faster. Our study, combining empirical evidence and theoretical results, not only provides nuanced insights into the differences between label smoothing and cross-entropy losses, but also serves as an example of how the powerful neural collapse framework can be used to improve our understanding of DNNs.

Pre-training with Synthetic Data Helps Offline Reinforcement Learning

Recently, it has been shown that for offline deep reinforcement learning (DRL), pre-training Decision Transformer with a large language corpus can improve downstream performance (Reid et al., 2022). A natural question to ask is whether this performance gain can only be achieved with language pre-training, or can be achieved with simpler pre-training schemes which do not involve language. In this paper, we first show that language is not essential for improved performance, and indeed pre-training with synthetic IID data for a small number of updates can match the performance gains from pre-training with a large language corpus; moreover, pre-training with data generated by a one-step Markov chain can further improve the performance. Inspired by these experimental results, we then consider pre-training Conservative Q-Learning (CQL), a popular offline DRL algorithm, which is Q-learning-based and typically employs a Multi-Layer Perceptron (MLP) backbone. Surprisingly, pre-training with simple synthetic data for a small number of updates can also improve CQL, providing consistent performance improvement on D4RL Gym locomotion datasets. The results of this paper not only illustrate the importance of pre-training for offline DRL but also show that the pre-training data can be synthetic and generated with remarkably simple mechanisms.

On the Convergence of Monte Carlo UCB for Random-Length Episodic MDPs

In reinforcement learning, Monte Carlo algorithms update the Q function by averaging the episodic returns. In the Monte Carlo UCB (MC-UCB) algorithm, the action taken in each state is the action that maximizes the Q function plus a UCB exploration term, which biases the choice of actions to those that have been chosen less frequently. Although there has been significant work on establishing regret bounds for MC-UCB, most of that work has been focused on finite-horizon versions of the problem, for which each episode terminates after a constant number of steps. For such finite-horizon problems, the optimal policy depends both on the current state and the time within the episode. However, for many natural episodic problems, such as games like Go and Chess and robotic tasks, the episode is of random length and the optimal policy is stationary. For such environments, it is an open question whether the Q-function in MC-UCB will converge to the optimal Q function; we conjecture that, unlike Q-learning, it does not converge for all MDPs. We nevertheless show that for a large class of MDPs, which includes stochastic MDPs such as blackjack and deterministic MDPs such as Go, the Q-function in MC-UCB converges almost surely to the optimal Q function. An immediate corollary of this result is that it also converges almost surely for all finite-horizon MDPs. We also provide numerical experiments, providing further insights into MC-UCB.

VRL3: A Data-Driven Framework for Visual Deep Reinforcement Learning

We propose a simple but powerful data-driven framework for solving highly challenging visual deep reinforcement learning (DRL) tasks. We analyze a number of major obstacles in taking a data-driven approach, and present a suite of design principles, training strategies, and critical insights about data-driven visual DRL. Our framework has three stages: in stage 1, we leverage non-RL datasets (e.g. ImageNet) to learn task-agnostic visual representations; in stage 2, we use offline RL data (e.g. a limited number of expert demonstrations) to convert the task-agnostic representations into more powerful task-specific representations; in stage 3, we fine-tune the agent with online RL. On a set of highly challenging hand manipulation tasks with sparse reward and realistic visual inputs, our framework learns 370%-1200% faster than the previous SOTA method while using an encoder that is 50 times smaller, fully demonstrating the potential of data-driven deep reinforcement learning.

Randomized Ensembled Double Q-Learning: Learning Fast Without a Model

Using a high Update-To-Data (UTD) ratio, model-based methods have recently achieved much higher sample efficiency than previous model-free methods for continuous-action DRL benchmarks. In this paper, we introduce a simple model-free algorithm, Randomized Ensembled Double Q-Learning (REDQ), and show that its performance is just as good as, if not better than, a state-of-the-art model-based algorithm for the MuJoCo benchmark. Moreover, REDQ can achieve this performance using fewer parameters than the model-based method, and with less wall-clock run time. REDQ has three carefully integrated ingredients which allow it to achieve its high performance: (i) a UTD ratio >> 1; (ii) an ensemble of Q functions; (iii) in-target minimization across a random subset of Q functions from the ensemble. Through carefully designed experiments, we provide a detailed analysis of REDQ and related model-free algorithms. To our knowledge, REDQ is the first successful model-free DRL algorithm for continuous-action spaces using a UTD ratio >> 1.

On the Convergence of the Monte Carlo Exploring Starts Algorithm for Reinforcement Learning

A simple and natural algorithm for reinforcement learning is Monte Carlo Exploring States (MCES), where the Q-function is estimated by averaging the Monte Carlo returns, and the policy is improved by choosing actions that maximize the current estimate of the Q-function. Exploration is performed by "exploring starts", that is, each episode begins with a randomly chosen state and action and then follows the current policy. Establishing convergence for this algorithm has been an open problem for more than 20 years. We make headway with this problem by proving convergence for Optimal Policy Feed-Forward MDPs, which are MDPs whose states are not revisited within any episode for an optimal policy. Such MDPs include all deterministic environments (including Cliff Walking and other gridworld examples) and a large class of stochastic environments (including Blackjack). The convergence results presented here make progress for this long-standing open problem in reinforcement learning.

BAIL: Best-Action Imitation Learning for Batch Deep Reinforcement Learning

The field of Deep Reinforcement Learning (DRL) has recently seen a surge in research in batch reinforcement learning, which aims for sample-efficient learning from a given data set without additional interactions with the environment. In the batch DRL setting, commonly employed off-policy DRL algorithms can perform poorly and sometimes even fail to learn altogether. In this paper, we propose a new algorithm, Best-Action Imitation Learning (BAIL), which unlike many off-policy DRL algorithms does not involve maximizing Q functions over the action space. Striving for simplicity as well as performance, BAIL first selects from the batch the actions it believes to be high-performing actions for their corresponding states; it then uses those state-action pairs to train a policy network using imitation learning. Although BAIL is simple, we demonstrate that BAIL achieves state of the art performance on the Mujoco benchmark.

Towards Simplicity in Deep Reinforcement Learning: Streamlined Off-Policy Learning

The field of Deep Reinforcement Learning (DRL) has recently seen a surge in the popularity of maximum entropy reinforcement learning algorithms. Their popularity stems from the intuitive interpretation of the maximum entropy objective and their superior sample efficiency on standard benchmarks. In this paper, we seek to understand the primary contribution of the entropy term to the performance of maximum entropy algorithms. For the Mujoco benchmark, we demonstrate that the entropy term in Soft Actor-Critic (SAC) principally addresses the bounded nature of the action spaces. With this insight, we propose a simple normalization scheme which allows a streamlined algorithm without entropy maximization match the performance of SAC. Our experimental results demonstrate a need to revisit the benefits of entropy regularization in DRL. We also propose a simple non-uniform sampling method for selecting transitions from the replay buffer during training. We further show that the streamlined algorithm with the simple non-uniform sampling scheme outperforms SAC and achieves state-of-the-art performance on challenging continuous control tasks.

Boosting Soft Actor-Critic: Emphasizing Recent Experience without Forgetting the Past

Soft Actor-Critic (SAC) is an off-policy actor-critic deep reinforcement learning (DRL) algorithm based on maximum entropy reinforcement learning. By combining off-policy updates with an actor-critic formulation, SAC achieves state-of-the-art performance on a range of continuous-action benchmark tasks, outperforming prior on-policy and off-policy methods. The off-policy method employed by SAC samples data uniformly from past experience when performing parameter updates. We propose Emphasizing Recent Experience (ERE), a simple but powerful off-policy sampling technique, which emphasizes recently observed data while not forgetting the past. The ERE algorithm samples more aggressively from recent experience, and also orders the updates to ensure that updates from old data do not overwrite updates from new data. We compare vanilla SAC and SAC+ERE, and show that ERE is more sample efficient than vanilla SAC for continuous-action Mujoco tasks. We also consider combining SAC with Priority Experience Replay (PER), a scheme originally proposed for deep Q-learning which prioritizes the data based on temporal-difference (TD) error. We show that SAC+PER can marginally improve the sample efficiency performance of SAC, but much less so than SAC+ERE. Finally, we propose an algorithm which integrates ERE and PER and show that this hybrid algorithm can give the best results for some of the Mujoco tasks.