We note that these results are about two of the most commonly used architecture modifications for RNNs. First, the gating mechanism is ubiquitous in RNNs, and usually thought of as a heuristic for smoothing optimization [28]. Second, many of the effective large-scale RNNs use linear (gated) recurrences and deeper models, which is usually thought of as a heuristic for computational efficiency [5]. Our results suggest that neither of these are heuristics after all, and arise from standard ways to approximate ODEs. To be more specific, we show that: 19 Table 6: A summary of the characteristics of popular RNN methods and their approximation mechanisms for capturing the dynamics x(t) = x(t) + f(t,x(t)) (equation (14)). The LSSL entries are for the very specific case with order N = 1 and A= 1,B = 1,C = 1,D= 0; LSSLs are more general.

We introduce a new approach for computing optimal equilibria and mechanisms via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated, communication, and certification equilibria. We observe that optimal equilibria are minimax equilibrium strategies of a player in an extensiveform zero-sum game. This reformulation allows us to apply techniques for learning in zero-sum games, yielding the first learning dynamics that converge to optimal equilibria, not only in empirical averages, but also in iterates. We demonstrate the practical scalability and flexibility of our approach by attaining state-of-the-art performance in benchmark tabular games, and by computing an optimal mechanism for a sequential auction design problem using deep reinforcement learning.

We introduce REDO, a class-agnostic framework to REconstruct the Dynamic Objects from RGBD or calibrated videos. Compared to prior work, our problem setting is more realistic yet more challenging for three reasons: 1) due to occlusion or camera settings an object of interest may never be entirely visible, but we aim to reconstruct the complete shape; 2) we aim to handle different object dynamics including rigid motion, non-rigid motion, and articulation; 3) we aim to reconstruct different categories of objects with one unified framework. To address these challenges, we develop two novel modules. First, we introduce a canonical 4D implicit function which is pixel-aligned with aggregated temporal visual cues. Second, we develop a 4D transformation module which captures object dynamics to support temporal propagation and aggregation. We study the efficacy of REDO in extensive experiments on synthetic RGBD video datasets SAIL-VOS 3D and DeformingThings4D++, and on real-world video data 3DPW. We find REDO outperforms state-of-the-art dynamic reconstruction methods by a margin. In ablation studies we validate each developed component.

We show that Deep Neural Networks introduce two heteroscedastic Gumbel noise sources into Q-Learning. To account for these noise sources, we propose Double Gumbel Q-Learning, a Deep Q-Learning algorithm applicable for both discrete and continuous control. In discrete control, we derive a closed-form expression for the loss function of our algorithm. In continuous control, this loss function is intractable and we therefore derive an approximation with a hyperparameter whose value regulates pessimism in Q-Learning. We present a default value for our pessimism hyperparameter that enables DoubleGum to outperform DDPG, TD3, SAC, XQL, quantile regression, and Mixture-of-Gaussian Critics in aggregate over 33 tasks from DeepMind Control, MuJoCo, MetaWorld, and Box2D and show that tuning this hyperparameter may further improve sample efficiency.