ETC1 with 3D/4D random-restart hill climbing

For fun, I implemented a full ETC1 block encoder using random-restart hill climbing, to see how it behaves compared to my current custom optimizer (the one in rg_etc1). This method works surprisingly well and is quite simple. (Note I'm switching to luma PSNR, because I've been using perceptually weighted color distance. My previous posts used average RGB PSNR.)

The number of attempts per block is fixed. The first 4D hill climb always starts at the subblock's average color, with an intensity table index of 3. The second 4D hill climb starts at a random color/intensity. (In differential mode, the 2nd subblock's hill climb position is constrained to lie near the first one, otherwise we can't code it.) Eventually, it switches from 4D to 3D hill climbing, by randomly climbing only within the best found intensity plane.

The nearly-best ETC1 encoding (using rg_etc1 - not hill climbing) was 38.053 dB:
Y: Error: Max:  38, Mean: 2.181, MSE: 10.181, RMSE: 3.191, PSNR: 38.053, SSIM: 0.983632

- 1 hill climb, 33.998 dB:

Y: Error: Max:  35, Mean: 3.943, MSE: 25.901, RMSE: 5.089, PSNR: 33.998, SSIM: 0.933979

- 2 hill climbs, 37.808 dB:

Y: Error: Max:  33, Mean: 2.281, MSE: 10.770, RMSE: 3.282, PSNR: 37.808, SSIM: 0.980324

- 4 hill climbs, 37.818 dB:

 Y: Error: Max:  33, Mean: 2.280, MSE: 10.748, RMSE: 3.278, PSNR: 37.818, SSIM: 0.980280

- 16 hill climbs, 37.919 dB:

Y: Error: Max:  38, Mean: 2.241, MSE: 10.499, RMSE: 3.240, PSNR: 37.919, SSIM: 0.981631

That 2nd random 4D hill climb helps a lot. Quality quickly plateaus however, at least on this image, and subsequent climbs don't add much. Very interestingly to me, even just 4 climbs nearly matches the quality of my hand-tuned ETC1 optimizer.