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We analyze Nash games played among leaders of Stackelberg games (NASP). We show it is Σ p 2 - hard to decide if the game has a mixed-strate… (voir plus)gy Nash equilibrium (MNE), even when there are only two leaders and each leader has one follower. We provide a finite time algorithm with a running time bounded by O (2 2 n ) which computes MNEs for NASP when it exists and returns infeasibility if no MNE exists. We also provide two ways to improve the algorithm which involves constructing a series of inner approximations (alternatively, outer approximations) to the leaders’ feasible region that will provably obtain the required MNE. Finally, we test our algorithms on a range of NASPs arising out of a game in the energy market, where countries act as Stackelberg leaders who play a Nash game, and the domestic producers act as the followers.
We consider stochastic second-order methods for minimizing smooth and strongly-convex functions under an interpolation condition satisfied b… (voir plus)y over-parameterized models. Under this condition, we show that the regularized subsampled Newton method (R-SSN) achieves global linear convergence with an adaptive step-size and a constant batch-size. By growing the batch size for both the subsampled gradient and Hessian, we show that R-SSN can converge at a quadratic rate in a local neighbourhood of the solution. We also show that R-SSN attains local linear convergence for the family of self-concordant functions. Furthermore, we analyze stochastic BFGS algorithms in the interpolation setting and prove their global linear convergence. We empirically evaluate stochastic L-BFGS and a "Hessian-free" implementation of R-SSN for binary classification on synthetic, linearly-separable datasets and real datasets under a kernel mapping. Our experimental results demonstrate the fast convergence of these methods, both in terms of the number of iterations and wall-clock time.
Drawing an inspiration from behavioral studies of human decision making, we propose here a general parametric framework for a reinforcement … (voir plus)learning problem, which extends the standard Q-learning approach to incorporate a two-stream framework of reward processing with biases biologically associated with several neurological and psychiatric conditions, including Parkinson's and Alzheimer's diseases, attention-deficit/hyperactivity disorder (ADHD), addiction, and chronic pain. For the AI community, the development of agents that react differently to different types of rewards can enable us to understand a wide spectrum of multi-agent interactions in complex real-world socioeconomic systems. Empirically, the proposed model outperforms Q-Learning and Double Q-Learning in artificial scenarios with certain reward distributions and real-world human decision making gambling tasks. Moreover, from the behavioral modeling perspective, our parametric framework can be viewed as a first step towards a unifying computational model capturing reward processing abnormalities across multiple mental conditions and user preferences in long-term recommendation systems.
Continuous control tasks in reinforcement learning are important because they provide an important framework for learning in high-dimensiona… (voir plus)l state spaces with deceptive rewards, where the agent can easily become trapped into suboptimal solutions. One way to avoid local optima is to use a population of agents to ensure coverage of the policy space, yet learning a population with the "best" coverage is still an open problem. In this work, we present a novel approach to population-based RL in continuous control that leverages properties of normalizing flows to perform attractive and repulsive operations between current members of the population and previously observed policies. Empirical results on the MuJoCo suite demonstrate a high performance gain for our algorithm compared to prior work, including Soft-Actor Critic (SAC).
In class-incremental learning, a model learns continuously from a sequential data stream in which new classes occur. Existing methods often … (voir plus)rely on static architectures that are manually crafted. These methods can be prone to capacity saturation because a neural network's ability to generalize to new concepts is limited by its fixed capacity. To understand how to expand a continual learner, we focus on the neural architecture design problem in the context of class-incremental learning: at each time step, the learner must optimize its performance on all classes observed so far by selecting the most competitive neural architecture. To tackle this problem, we propose Continual Neural Architecture Search (CNAS): an autoML approach that takes advantage of the sequential nature of class-incremental learning to efficiently and adaptively identify strong architectures in a continual learning setting. We employ a task network to perform the classification task and a reinforcement learning agent as the meta-controller for architecture search. In addition, we apply network transformations to transfer weights from previous learning step and to reduce the size of the architecture search space, thus saving a large amount of computational resources. We evaluate CNAS on the CIFAR-100 dataset under varied incremental learning scenarios with limited computational power (1 GPU). Experimental results demonstrate that CNAS outperforms architectures that are optimized for the entire dataset. In addition, CNAS is at least an order of magnitude more efficient than naively using existing autoML methods.
