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Open Access Publications from the University of California

Scholarly Works (5 results)

  • Article
  • Peer Reviewed
UCLA Previously Published Works (2019)
We revisit the natural gradient method for learning in statistical manifolds. We consider the proximal formulation and obtain a closed form approximation of the proximity term over an affine subspace of functions in the Legendre dual formulation. We consider two important types of statistical metrics, namely the Wasserstein and Fisher-Rao metrics, and introduce numerical methods for high dimensional parameter spaces.
    • Thesis
    • Peer Reviewed
    UCLA Electronic Theses and Dissertations (2020)

    In this dissertation, we provide efficient algorithms for modeling the behavior of a single agent, multiple agents, and a continuum of agents. For a single agent, we combine the modeling framework of optimal control with advances in optimization splitting in order to efficiently find optimal paths for problems in very high-dimensions, thus providing alleviation from the curse of dimensionality. For a multiple, but finite, number of agents, we take the framework of multi-agent reinforcement learning and utilize imitation learning in order to decentralize a centralized expert, thus obtaining optimal multi-agents that act in a decentralized fashion. For a continuum of agents, we take the framework of mean-field games and use two neural networks, which we train in an alternating scheme, in order to efficiently find optimal paths for high-dimensional and stochastic problems. These tools cover a wide variety of use-cases that can be immediately deployed for practical applications.

      Cover page: Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents
      • Article
      • Peer Reviewed
      UCLA Previously Published Works (2019)
        • Article
        • Peer Reviewed
        UCLA Previously Published Works (2019)
        We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and define a corresponding input-dependent additive noise data augmentation model. Expanding and integrating the augmented loss yields an effective Tikhonov-type Wasserstein diffusion smoothness regularizer. This approach allows us to apply high levels of regularization and train functions that have low variability within classes but remain flexible across classes. We provide efficient methods for computing the regularizer at a negligible cost in comparison to training with adversarial data augmentation. Initial experiments demonstrate improvements in generalization performance under adversarial perturbations and also large in-class variations of the input data.
          • Article
          • Peer Reviewed
          UCLA Previously Published Works (2021)
          We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean-field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are not approachable with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex-concave saddle-point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN). We show the potential of our method on up to 100-dimensional MFG problems.
            Cover page: Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games
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