Papers

To solve optimization problems with nonlinear constrains, the recently developed Riemannian meta-optimization methods show promise, which train neural networks as an optimizer to perform optimization on Riemannian manifolds. A key challenge is the heavy computational and memory burdens, because computing the meta-gradient with respect to the optimizer involves a series of time-consuming derivatives, and stores large computation graphs in memory. In this paper, we propose an efficient Riemannian meta-optimization method that decouples the complex computation scheme from the meta-gradient. We derive Riemannian implicit differentiation to compute the meta-gradient by establishing a link between Riemannian optimization and the implicit function theorem. As a result, the updating our optimizer is only related to the final two iterations, which in turn speeds up our method and reduces the memory footprint significantly. We theoretically study the computational load and memory footprint of our method for long optimization trajectories, and conduct an empirical study to demonstrate the benefits of the proposed method. Evaluations of three optimization problems on different Riemannian manifolds show that our method achieves state-of-the-art performance in terms of the convergence speed and the quality of optima.

poster session 2 @ blue 1, poster session 9 @ blue 1, oral session 2 @ blue 1, poster session 2, poster session 9, oral session 2

Optimizing a machine learning (ML) pipeline has been an important topic of AI and ML. Despite recent progress, pipeline optimization remains a challenging problem, due to potentially many combinations to consider as well as slow training and validation. We present the BLDS algorithm for optimized algorithm selection (ML operations) in a fixed ML pipeline structure. BLDS performs multi-fidelity optimization for selecting ML algorithms trained with smaller computational overhead, while controlling its pipeline search based on multi-armed bandit and limited discrepancy search. Our experiments on well-known classification benchmarks show that BLDS is superior to competing algorithms. We also combine BLDS with hyperparameter optimization, empirically showing the advantage of BLDS.

poster session 2 @ blue 1, poster session 9 @ blue 1, oral session 2 @ blue 1, poster session 2, poster session 9, oral session 2

Reactive synthesis from high-level specifications that combine {\em hard} constraints expressed in Linear Temporal Logic ($\ltl$) with {\em soft} constraints expressed by discounted-sum (DS) rewards has applications in planning and reinforcement learning. An existing approach combines techniques from $\ltl$ synthesis with optimization for the DS rewards but has failed to yield a sound algorithm. An alternative approach combining $\ltl$ synthesis with satisficing DS rewards (rewards that achieve a threshold) is sound and complete for integer discount factors, but, in practice, a fractional discount factor is desired. This work extends the existing satisficing approach, presenting the first sound algorithm for synthesis from $\ltl$ and DS rewards with fractional discount factors. The utility of our algorithm is demonstrated on robotic planning domains.

poster session 2 @ blue 1, poster session 9 @ blue 1, oral session 2 @ blue 1, poster session 2, poster session 9, oral session 2