The obvious alternative to gradient descent here would be Bayes Formula (probabalistic Bayesian belief updates), since this addresses the exact problem that our brains evolved to optimize - how to utilize prediction failure (sensory feedback vs prediction) to make better predictions - better prediction of where the food is, what the predator will do, how to attract a mate, etc. Predict next word too (learn language), of course.

I don't think pre-train for every update works - it's an incredibly slow and expensive way to learn, and the training data just isn't there. Where is the training data that could train it how to do every aspect of any job - the stuff that humans learn by experimentation and experience? The training data that is available via text (and video) is mostly artifacts - what someone created, not the thought process that went into creating it, and the failed experiments and pitfalls to avoid along the way, etc, etc.

It would be nice to have a generic college-graduate pre-trained AGI as a starting point, but then you need to take that and train it how to be a developer (starting at entry level, etc), or for whatever job you'd like it to do. It takes a human years to practice to get good at jobs like these, with many try-fail-rethink experiments every day. Imagine if each of those daily updates took 6 months and $100M to incorporate?! We really need genuine online learning where each generic graduate-level AGI instance can get on-the-job training and human feedback and update it's own "weights" continually.