Unlike humans, who are capable of continual learning over their lifetimes, artificial neural networks have long been known to suffer from a phenomenon known as catastrophic forgetting, whereby new learning can lead to abrupt erasure of previously acquired knowledge. Whereas in a neural network the parameters are typically modelled as scalar values, an individual synapse in the brain comprises a complex network of interacting biochemical components that evolve at different timescales. In this paper, we show that by equipping tabular and deep reinforcement learning agents with a synaptic model that incorporates this biological complexity (Benna & Fusi, 2016), catastrophic forgetting can be mitigated at multiple timescales. In particular, we find that as well as enabling continual learning across sequential training of two simple tasks, it can also be used to overcome within-task forgetting by reducing the need for an experience replay database.
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm. We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning algorithm, network architecture and hyper-parameters, our algorithm robustly solves more than 20 simulated physics tasks, including classic problems such as cartpole swing-up, dexterous manipulation, legged locomotion and car driving. Our algorithm is able to find policies whose performance is competitive with those found by a planning algorithm with full access to the dynamics of the domain and its derivatives. We further demonstrate that for many of the tasks the algorithm can learn policies end-to-end: directly from raw pixel inputs. The biological mechanisms underlying memory are complex and typically involve multiple molecular processes operating on timescales ranging from fractions of a second to years. The authors show using a mathematical model of synaptic plasticity and consolidation that this complexity can help explain the formidable memory capacity of biological systems.  A new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated. Convergence with probability one is proved for a variety of classical optimization and identification problems. It is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence.