Reconfigurable Intelligent Surfaces (RISs) offer a promising means of reshaping the wireless propagation environment, yet practical methods for configuring large passive arrays to achieve reliable signal equalization remain limited. Equalization is essential in wideband links to counteract multipath-induced pulse distortion that otherwise degrades symbol recovery. This work investigates RIS-assisted pulse response equalization and signal boosting using both classical adaptive filtering and model-free deep reinforcement learning (DRL). We develop a steepest descent (SD) method that exploits cascaded BS-RIS-UE channel information to configure RIS coefficients for multipath mitigation and SNR enhancement, and we show that the tradeoffs between SD and DRL primarily arise from the extensive channel estimation required for accurate equalization with passive RIS hardware. Unlike traditional adaptive filtering, which updates delayed filter coefficients after signal reception, our approach uses the RIS positioned within the cascaded channel to perform equalization without delay elements, prior to reception at the UE. In this framework, the channel is estimated before equalization, forming the basis of what we term adaptive RIS equalization (ARISE). To overcome the reliance on channel estimation required for ARISE, we explore several DRL algorithms -- DDPG, TD3, and SAC -- that optimize RIS coefficients directly from the received pulse response without explicit channel estimation. Through extensive simulations across diverse channel conditions and RIS sizes, we show that SAC achieves fast, stable convergence and equalization performance comparable to ARISE while offering significantly lower implementation complexity. These results highlight the potential of DRL as a practical and scalable solution for real-time RIS control in future wireless systems.