We introduce the polymer analysis and discovery array (PANDA), an automated system for high-throughput electrodeposition and functional characterization of polymer films. The PANDA is a custom, modular, and low-cost system based on a CNC gantry that we have modified to include a syringe pump, potentiostat, and camera with a telecentric lens. This system can perform fluid handling, electrochemistry, and transmission optical measurements on samples in custom 96-well plates that feature transparent and conducting bottoms. We begin by validating this platform through a series of control fluid handling and electrochemistry experiments to quantify the repeatability, lack of cross-contamination, and accuracy of the system. As a proof-of-concept experimental campaign to study the functional properties of a model polymer film, we optimize the electrochromic switching of electrodeposited poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) films. In particular, we explore the monomer concentration, deposition time, and deposition voltage using an array of experiments selected by Latin hypercube sampling. Subsequently, we run an active learning campaign based upon Bayesian optimization to find the processing conditions that lead to the highest electrochromic switching of PEDOT:PSS. This self-driving lab integrates optical and electrochemical characterization to constitute a novel, automated approach for studying functional polymer films.