| """ |
| CMA-ES on step function heights with SMALL N_eval for speed. |
| Then upsample and polish. |
| """ |
| import sys |
| import numpy as np |
| import cma |
| import jax |
| import jax.numpy as jnp |
| import optax |
| from scipy.optimize import minimize as scipy_minimize |
|
|
|
|
| def compute_c1_fast(f, dx): |
| n = len(f) |
| padded = np.zeros(2 * n) |
| padded[:n] = f |
| fft_f = np.fft.rfft(padded) |
| conv = np.fft.irfft(fft_f * fft_f, n=2*n) * dx |
| integral_sq = (np.sum(f) * dx) ** 2 |
| if integral_sq < 1e-12: |
| return 1e10 |
| return np.max(conv) / integral_sq |
|
|
|
|
| def compute_c1_numpy(f_values, n_points): |
| dx = 0.5 / n_points |
| f_nn = np.maximum(f_values, 0.0) |
| autoconv = np.convolve(f_nn, f_nn, mode='full') * dx |
| integral_sq = (np.sum(f_nn) * dx) ** 2 |
| if integral_sq < 1e-12: |
| return 1e10 |
| return np.max(autoconv) / integral_sq |
|
|
|
|
| def step_to_fine(heights, N_eval): |
| K = len(heights) |
| f = np.zeros(N_eval) |
| for i in range(K): |
| s = int(i * N_eval / K) |
| e = int((i + 1) * N_eval / K) |
| f[s:e] = max(heights[i], 0.0) |
| return f |
|
|
|
|
| def run_cma(K, N_eval, seed=42, maxiter=5000, popsize=None): |
| dx = 0.5 / N_eval |
| if popsize is None: |
| popsize = max(50, 4 + int(3 * np.log(K))) |
|
|
| def objective(log_heights): |
| heights = np.exp(np.clip(log_heights, -4, 4)) |
| f = step_to_fine(heights, N_eval) |
| return compute_c1_fast(f, dx) |
|
|
| x0 = np.zeros(K) |
|
|
| opts = { |
| 'maxiter': maxiter, |
| 'tolfun': 1e-14, |
| 'tolx': 1e-14, |
| 'popsize': popsize, |
| 'seed': seed, |
| 'verbose': -9, |
| } |
|
|
| es = cma.CMAEvolutionStrategy(x0, 1.0, opts) |
|
|
| gen = 0 |
| while not es.stop(): |
| solutions = es.ask() |
| fitnesses = [objective(s) for s in solutions] |
| es.tell(solutions, fitnesses) |
| gen += 1 |
| if gen % 500 == 0: |
| bf = es.result[1] |
| sys.stdout.write(f" Gen {gen}: best={bf:.10f}\n") |
| sys.stdout.flush() |
|
|
| best = es.result[0] |
| return np.exp(np.clip(best, -4, 4)), es.result[1] |
|
|
|
|
| def jax_polish(f_init, N, adam_steps=50000): |
| dx = 0.5 / N |
|
|
| @jax.jit |
| def obj_smooth(params, temp): |
| f = jnp.exp(jnp.clip(params, -8, 4)) |
| padded = jnp.zeros(2 * N) |
| padded = padded.at[:N].set(f) |
| fft_f = jnp.fft.rfft(padded) |
| conv = jnp.fft.irfft(fft_f * fft_f, n=2 * N) * dx |
| integral_sq = (jnp.sum(f) * dx) ** 2 |
| smooth_max = jax.nn.logsumexp(temp * conv) / temp |
| return smooth_max / integral_sq |
|
|
| @jax.jit |
| def obj_hard(params): |
| f = jnp.exp(jnp.clip(params, -8, 4)) |
| padded = jnp.zeros(2 * N) |
| padded = padded.at[:N].set(f) |
| fft_f = jnp.fft.rfft(padded) |
| conv = jnp.fft.irfft(fft_f * fft_f, n=2 * N) * dx |
| integral_sq = (jnp.sum(f) * dx) ** 2 |
| return jnp.max(conv) / integral_sq |
|
|
| grad_smooth = jax.jit(jax.grad(obj_smooth)) |
| grad_hard = jax.jit(jax.grad(obj_hard)) |
|
|
| params = jnp.array(np.log(np.maximum(f_init, 1e-6))) |
|
|
| lr_schedule = optax.warmup_cosine_decay_schedule( |
| init_value=0.0, peak_value=0.003, warmup_steps=1000, |
| decay_steps=adam_steps - 1000, end_value=1e-7, |
| ) |
| optimizer = optax.adam(learning_rate=lr_schedule) |
| opt_state = optimizer.init(params) |
|
|
| best_c1 = float('inf') |
| best_params = params |
|
|
| for step in range(adam_steps): |
| loss, grads = jax.value_and_grad(obj_smooth)(params, 300.0) |
| updates, opt_state = optimizer.update(grads, opt_state, params) |
| params = optax.apply_updates(params, updates) |
|
|
| if step % 10000 == 0 or step == adam_steps - 1: |
| hc = float(obj_hard(params)) |
| sys.stdout.write(f" Adam {step:6d}: C1={hc:.10f}\n") |
| sys.stdout.flush() |
| if hc < best_c1: |
| best_c1 = hc |
| best_params = params |
|
|
| |
| params_np = np.array(best_params, dtype=np.float64) |
| for temp in [1000.0, 10000.0]: |
| def scipy_obj(p): |
| p_jax = jnp.array(p) |
| val = float(obj_smooth(p_jax, temp)) |
| g = np.array(grad_smooth(p_jax, temp), dtype=np.float64) |
| return val, g |
| result = scipy_minimize( |
| scipy_obj, params_np, method='L-BFGS-B', jac=True, |
| options={'maxiter': 5000, 'ftol': 1e-15, 'gtol': 1e-14, 'maxcor': 50}, |
| ) |
| params_np = result.x |
|
|
| def scipy_obj_hard(p): |
| p_jax = jnp.array(p) |
| val = float(obj_hard(p_jax)) |
| g = np.array(grad_hard(p_jax), dtype=np.float64) |
| return val, g |
| result = scipy_minimize( |
| scipy_obj_hard, params_np, method='L-BFGS-B', jac=True, |
| options={'maxiter': 10000, 'ftol': 1e-16, 'gtol': 1e-15, 'maxcor': 100}, |
| ) |
| params_np = result.x |
|
|
| f_final = np.exp(np.clip(params_np, -8, 4)) |
| c1_final = compute_c1_numpy(f_final, N) |
| sys.stdout.write(f" After L-BFGS: C1={c1_final:.10f}\n") |
| sys.stdout.flush() |
| return f_final, c1_final |
|
|
|
|
| def run(): |
| best_c1 = float('inf') |
| best_f = None |
| best_n = None |
|
|
| N_coarse = 200 |
|
|
| |
| sys.stdout.write("Phase 1: CMA-ES on step functions\n") |
| sys.stdout.flush() |
|
|
| best_heights = None |
| best_cma_c1 = float('inf') |
|
|
| for K in [20, 30, 40, 50, 60, 80, 100]: |
| for seed in [42, 0, 7, 123, 99]: |
| heights, c1 = run_cma(K, N_coarse, seed=seed, maxiter=5000, popsize=80) |
| f = step_to_fine(heights, N_coarse) |
| c1v = compute_c1_fast(f, 0.5 / N_coarse) |
|
|
| if c1v < best_cma_c1: |
| best_cma_c1 = c1v |
| best_heights = heights.copy() |
| best_K = K |
| sys.stdout.write(f" K={K} seed={seed}: C1={c1v:.10f} ***\n") |
| elif seed == 42: |
| sys.stdout.write(f" K={K} seed={seed}: C1={c1v:.10f}\n") |
| sys.stdout.flush() |
|
|
| sys.stdout.write(f"\nBest CMA-ES: C1={best_cma_c1:.10f} with K={best_K}\n") |
| sys.stdout.flush() |
|
|
| |
| N_fine = 4000 |
| f_up = step_to_fine(best_heights, N_fine) |
| sys.stdout.write(f"\nPhase 2: Polish at N={N_fine}\n") |
| sys.stdout.flush() |
|
|
| f_polished, c1_polished = jax_polish(f_up, N_fine, adam_steps=60000) |
| sys.stdout.write(f" Polished: C1={c1_polished:.10f}\n") |
| sys.stdout.flush() |
|
|
| if c1_polished < best_c1: |
| best_c1 = c1_polished |
| best_f = f_polished |
| best_n = N_fine |
|
|
| |
| sys.stdout.write(f"\nPhase 3: Direct JAX seed 15 at N={N_fine}\n") |
| sys.stdout.flush() |
|
|
| np.random.seed(15) |
| init_f = np.ones(N_fine) * 0.5 + 0.02 * np.random.randn(N_fine) |
| f_direct, c1_direct = jax_polish(init_f, N_fine, adam_steps=80000) |
| sys.stdout.write(f" Direct: C1={c1_direct:.10f}\n") |
| sys.stdout.flush() |
|
|
| if c1_direct < best_c1: |
| best_c1 = c1_direct |
| best_f = f_direct |
| best_n = N_fine |
|
|
| sys.stdout.write(f"\nFinal C1: {best_c1:.10f}\n") |
| sys.stdout.flush() |
| return best_f, best_c1, best_c1, best_n |
|
|
