This paper investigates the joint optimization of the transmit precoder and the transmission/reflection coefficients of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) to maximize the weighted sum rate (WSR) in a multi-user downlink. We propose a particle-swarm-assisted gradient meta-learning (PSA-GML) algorithm for this non-convex problem. The original problem is first equivalently transformed via an amplitude-split parameterization and a collapsed precoder representation, which automatically satisfy the energy-conservation constraint and reduce the search dimension. Particle swarm optimization (PSO) then performs a global search over the STAR-RIS coefficients to yield a high-quality, initialization-robust warm start, with the transmit precoder obtained in closed form. Departing from conventional alternating optimization (AO), a coordinate-wise long short-term memory (LSTM) meta-optimizer trained by first-order gradient meta-learning further refines the coefficients and precoder jointly, learning per-coordinate adaptive update rules from data. The meta-optimizer is trained offline and applied to unseen channels without further adaptation. Numerical results show that PSA-GML attains an 11.06 bits/s/Hz WSR at 10 dB with N=32 elements and K=4 users, exceeding AO by 13.1% (and by 6.2% even with multiple random restarts) and the random-phase scheme by 35.1%. In the interference-limited regime it reaches 83.9% of the hand-designed Adam refinement without manual hyper-parameter tuning, and it transfers zero-shot across regimes, indicating that the learned update rule captures the intrinsic WSR landscape structure.

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