Manan Gandhi

Manan Gandhi, Yunpeng Pan, Evangelos Theodorou

Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of model knowledge can be overcome with machine learning techniques, utilizing measurements to build a dynamical model from the data. This paper aims to take the middle ground between these two approaches by introducing a semi-parametric representation of the underlying system dynamics. Our goal is to leverage the considerable information contained in a traditional physics based model and combine it with a data-driven, non-parametric regression technique known as a Gaussian Process. Integrating this semi-parametric model with model predictive pseudospectral control, we demonstrate this technique on both a cart pole and quadrotor simulation with unmodeled damping and parametric error. In order to manage parametric uncertainty, we introduce an algorithm that utilizes Sparse Spectrum Gaussian Processes (SSGP) for online learning after each rollout. We implement this online learning technique on a cart pole and quadrator, then demonstrate the use of online learning and obstacle avoidance for the dubin vehicle dynamics.

Shahriar Golchin, Yanfei Chen, Rujun Han et al.

Long-context large language models (LLMs) are able to process inputs containing up to several million tokens. In the scope of in-context learning (ICL), this translates into using hundreds/thousands of demonstrations in the input prompt, enabling many-shot ICL. In practice, a fixed set of demonstrations is often selected at random in many-shot settings due to (1) high inference costs, (2) the benefits of caching and reusing computations, and (3) the similar performance offered by this strategy compared to others when scaled. In this work, we propose two straightforward strategies for demonstration selection in many-shot ICL that improve performance with minimal computational overhead. Our first method combines a small number of demonstrations, selected based on their similarity to each test sample, with a disproportionately larger set of random demonstrations that are cached. The second strategy improves the first by replacing random demonstrations with those selected using centroids derived from test sample representations via k-means clustering. Our experiments with Gemini Pro and Flash across several datasets indicate that our strategies consistently outperform random selection and surpass or match the most performant selection approach while supporting caching and reducing inference cost by up to an order of magnitude. We also show that adjusting the proportion of demonstrations selected based on different criteria can balance performance and inference cost in many-shot ICL.

Yikun Cheng, Pan Zhao, Manan Gandhi et al.

A reinforcement learning (RL) policy trained in a nominal environment could fail in a new/perturbed environment due to the existence of dynamic variations. Existing robust methods try to obtain a fixed policy for all envisioned dynamic variation scenarios through robust or adversarial training. These methods could lead to conservative performance due to emphasis on the worst case, and often involve tedious modifications to the training environment. We propose an approach to robustifying a pre-trained non-robust RL policy with $\mathcal{L}_1$ adaptive control. Leveraging the capability of an $\mathcal{L}_1$ control law in the fast estimation of and active compensation for dynamic variations, our approach can significantly improve the robustness of an RL policy trained in a standard (i.e., non-robust) way, either in a simulator or in the real world. Numerical experiments are provided to validate the efficacy of the proposed approach.

Manan Gandhi, Keuntaek Lee, Yunpeng Pan et al.

Many neural networks use the tanh activation function, however when given a probability distribution as input, the problem of computing the output distribution in neural networks with tanh activation has not yet been addressed. One important example is the initialization of the echo state network in reservoir computing, where random initialization of the reservoir requires time to wash out the initial conditions, thereby wasting precious data and computational resources. Motivated by this problem, we propose a novel solution utilizing a moment based approach to propagate uncertainty through an Echo State Network to reduce the washout time. In this work, we contribute two new methods to propagate uncertainty through the tanh activation function and propose the Probabilistic Echo State Network (PESN), a method that is shown to have better average performance than deterministic Echo State Networks given the random initialization of reservoir states. Additionally we test single and multi-step uncertainty propagation of our method on two regression tasks and show that we are able to recover similar means and variances as computed by Monte-Carlo simulations.