Ruipeng Liu

Ruipeng Liu, Qinru Qiu, Simon Khan et al.

A computational bottleneck in current Vector-Symbolic Architectures (VSAs) is the ``clean-up'' step, which decodes the noisy vectors retrieved from the architecture. Clean-up typically compares noisy vectors against a ``codebook'' of prototype vectors, incurring computational complexity that is quadratic or similar. We present a new codebook representation that supports efficient clean-up, based on Kroneker products of rotation-like matrices. The resulting clean-up time complexity is linearithmic, i.e. $\mathcal{O}(N\,\text{log}\,N)$, where $N$ is the vector dimension and also the number of vectors in the codebook. Clean-up space complexity is $\mathcal{O}(N)$. Furthermore, the codebook is not stored explicitly in computer memory: It can be represented in $\mathcal{O}(\text{log}\,N)$ space, and individual vectors in the codebook can be materialized in $\mathcal{O}(N)$ time and space. At the same time, asymptotic memory capacity remains comparable to standard approaches. Computer experiments confirm these results, demonstrating several orders of magnitude more scalability than baseline VSA techniques.

Xulin Chen, Ruipeng Liu, Zhenyu Gan et al.

Uncertainties in transition dynamics pose a critical challenge in reinforcement learning (RL), often resulting in performance degradation of trained policies when deployed on hardware. Many robust RL approaches follow two strategies: enforcing smoothness in actor or actor-critic modules with Lipschitz regularization, or learning robust Bellman operators. However, the first strategy does not investigate the impact of critic-only Lipschitz regularization on policy robustness, while the second lacks comprehensive validation in real-world scenarios. Building on this gap and prior work, we propose PPO-PGDLC, an algorithm based on Proximal Policy Optimization (PPO) that integrates Projected Gradient Descent (PGD) with a Lipschitz-regularized critic (LC). The PGD component calculates the adversarial state within an uncertainty set to approximate the robust Bellman operator, and the Lipschitz-regularized critic further improves the smoothness of learned policies. Experimental results on two classic control tasks and one real-world robotic locomotion task demonstrates that, compared to several baseline algorithms, PPO-PGDLC achieves better performance and predicts smoother actions under environmental perturbations.