Jeongho Kim

Seokeon Choi, Sunghyun Park, Hyoungwoo Park et al.

Memory-efficient personalization is critical for adapting text-to-image diffusion models while preserving user privacy and operating within the limited computational resources of edge devices. To this end, we propose a selective optimization framework that adaptively chooses between backpropagation on low-resolution images (BP-low) and zeroth-order optimization on high-resolution images (ZO-high), guided by the characteristics of the diffusion process. As observed in our experiments, BP-low efficiently adapts the model to target-specific features, but suffers from structural distortions due to resolution mismatch. Conversely, ZO-high refines high-resolution details with minimal memory overhead but faces slow convergence when applied without prior adaptation. By complementing both methods, our framework leverages BP-low for effective personalization while using ZO-high to maintain structural consistency, achieving memory-efficient and high-quality fine-tuning. To maximize the efficacy of both BP-low and ZO-high, we introduce a timestep-aware probabilistic function that dynamically selects the appropriate optimization strategy based on diffusion timesteps. This function mitigates the overfitting from BP-low at high timesteps, where structural information is critical, while ensuring ZO-high is applied more effectively as training progresses. Experimental results demonstrate that our method achieves competitive performance while significantly reducing memory consumption, enabling scalable, high-quality on-device personalization without increasing inference latency.

Jeongho Kim, Jaeuk Shin, Insoon Yang

In this paper, we propose Q-learning algorithms for continuous-time deterministic optimal control problems with Lipschitz continuous controls. Our method is based on a new class of Hamilton-Jacobi-Bellman (HJB) equations derived from applying the dynamic programming principle to continuous-time Q-functions. A novel semi-discrete version of the HJB equation is proposed to design a Q-learning algorithm that uses data collected in discrete time without discretizing or approximating the system dynamics. We identify the condition under which the Q-function estimated by this algorithm converges to the optimal Q-function. For practical implementation, we propose the Hamilton-Jacobi DQN, which extends the idea of deep Q-networks (DQN) to our continuous control setting. This approach does not require actor networks or numerical solutions to optimization problems for greedy actions since the HJB equation provides a simple characterization of optimal controls via ordinary differential equations. We empirically demonstrate the performance of our method through benchmark tasks and high-dimensional linear-quadratic problems.

Jeongho Kim, Insoon Yang

In this paper, we introduce Hamilton-Jacobi-Bellman (HJB) equations for Q-functions in continuous time optimal control problems with Lipschitz continuous controls. The standard Q-function used in reinforcement learning is shown to be the unique viscosity solution of the HJB equation. A necessary and sufficient condition for optimality is provided using the viscosity solution framework. By using the HJB equation, we develop a Q-learning method for continuous-time dynamical systems. A DQN-like algorithm is also proposed for high-dimensional state and control spaces. The performance of the proposed Q-learning algorithm is demonstrated using 1-, 10- and 20-dimensional dynamical systems.