Gilad Karpel

Gilad Karpel, Ruida Zhou, Shoham Sabach et al.

Proximal Policy Optimization (PPO) is widely regarded as one of the most successful deep reinforcement learning algorithms, known for its robustness and effectiveness across a range of problems. The PPO objective encourages the importance ratio between the current and behavior policies to move to the "right" direction -- starting from importance sampling ratios equal to 1, increasing the ratios for actions with positive advantages and decreasing those with negative advantages. A clipping function is introduced to prevent over-optimization when updating the importance ratio in these "right" direction regions. Many PPO variants have been proposed to extend its success, most of which modify the objective's behavior by altering the clipping in the "right" direction regions. However, due to randomness in the rollouts and stochasticity of the policy optimization, we observe that the ratios frequently move to the "wrong" direction during the PPO optimization. This is a key factor hindering the improvement of PPO, but it has been largely overlooked. To address this, we propose the Directional-Clamp PPO algorithm (DClamp-PPO), which further penalizes the actions going to the strict "wrong" direction regions, where the advantage is positive (negative) and importance ratio falls below (above) $1 - β$ ($1+β$), for a tunable parameter $β\in (0, 1)$. The penalty is by enforcing a steeper loss slope, i.e., a clamp, in those regions. We demonstrate that DClamp-PPO consistently outperforms PPO, as well as its variants, by focusing on modifying the objective's behavior in the "right" direction, across various MuJoCo environments, using different random seeds. The proposed method is shown, both theoretically and empirically, to better avoid "wrong" direction updates while keeping the importance ratio closer to 1.

Gilad Karpel, Edward Moroshko, Ran Levinstein et al.

We study generalization in an overparameterized continual linear regression setting, where a model is trained with L2 (isotropic) regularization across a sequence of tasks. We derive a closed-form expression for the expected generalization loss in the high-dimensional regime that holds for arbitrary linear teachers. We demonstrate that isotropic regularization mitigates label noise under both single-teacher and multiple i.i.d. teacher settings, whereas prior work accommodating multiple teachers either did not employ regularization or used memory-demanding methods. Furthermore, we prove that the optimal fixed regularization strength scales nearly linearly with the number of tasks $T$, specifically as $T/\ln T$. To our knowledge, this is the first such result in theoretical continual learning. Finally, we validate our theoretical findings through experiments on linear regression and neural networks, illustrating how this scaling law affects generalization and offering a practical recipe for the design of continual learning systems.