scripts/aqm.py

"""
Independent reproduction of AQM (Adaptive Quasimetric Mapping), ICML 2026 #23758.

No official code / arXiv exists. Method reconstructed from the OpenReview abstract and
the authors' predecessor paper ProQ/PQP (arXiv:2506.18847): a time-to-reach quasimetric
(IQE + QRL-style loss) is learned from an offline dataset; AQM's novelties are
 (1) a sparse keypoint cover built as a greedy approximation to a dominating-set problem,
 (2) graph planning over those keypoints,
 (3) zero-shot replanning by pruning edges whose observed traversal time exceeds a
     time-to-reach budget derived from the quasimetric.

Env: 2D continuous point-mass mazes (OGBench pointmaze-style layouts). The low-level
controller is a shared oracle waypoint-follower for ALL methods, isolating the
graph-level claims from policy learning quality.
"""
import numpy as np
import torch
import torch.nn as nn
import time
import heapq

# ---------------------------------------------------------------- mazes
# Procedurally generated braided mazes: recursive backtracker (guaranteed
# connected) + removal of a fraction of walls to create loops, so that
# test-time blocking leaves alternative routes (needed for Claim 3).
def gen_maze(n_cells, seed, braid=0.35):
    rng = np.random.default_rng(seed)
    H = W = 2 * n_cells + 1
    g = np.ones((H, W), dtype=int)
    def carve(r, c):
        g[r, c] = 0
        dirs = [(0, 2), (0, -2), (2, 0), (-2, 0)]
        rng.shuffle(dirs)
        for dr, dc in dirs:
            nr, nc = r + dr, c + dc
            if 1 <= nr < H - 1 and 1 <= nc < W - 1 and g[nr, nc] == 1:
                g[r + dr // 2, c + dc // 2] = 0
                carve(nr, nc)
    import sys as _s
    _s.setrecursionlimit(10000)
    carve(1, 1)
    # braid: open some interior walls that separate two corridors
    walls = [(r, c) for r in range(1, H - 1) for c in range(1, W - 1)
             if g[r, c] == 1 and ((g[r - 1, c] == 0 and g[r + 1, c] == 0) or
                                  (g[r, c - 1] == 0 and g[r, c + 1] == 0))]
    rng.shuffle(walls)
    for r, c in walls[:int(len(walls) * braid)]:
        g[r, c] = 0
    return ["".join(str(x) for x in row) for row in g]

MAZES = {
    "medium": gen_maze(4, seed=7),    # 9x9
    "large": gen_maze(6, seed=11),    # 13x13
    "giant": gen_maze(8, seed=13),    # 17x17
}
CELL = 1.0  # cell size


class Maze:
    def __init__(self, name, extra_walls=()):
        self.grid = np.array([[int(c) for c in row] for row in MAZES[name]])
        self.name = name
        self.extra = set(extra_walls)  # set of (r, c) blocked at test time

    def blocked_cell(self, r, c):
        if r < 0 or c < 0 or r >= self.grid.shape[0] or c >= self.grid.shape[1]:
            return True
        return self.grid[r, c] == 1 or (r, c) in self.extra

    def blocked(self, xy):
        return self.blocked_cell(int(xy[1] // CELL), int(xy[0] // CELL))

    def free_cells(self):
        return [(r, c) for r in range(self.grid.shape[0])
                for c in range(self.grid.shape[1]) if not self.blocked_cell(r, c)]

    def cell_center(self, rc):
        return np.array([rc[1] + 0.5, rc[0] + 0.5]) * CELL

    def step(self, pos, vel, dt=1.0, max_speed=0.25):
        """Move with collision: sub-step and stop at walls."""
        v = np.clip(vel, -max_speed, max_speed)
        p = pos.copy()
        for _ in range(4):
            q = p + v * dt / 4
            if not self.blocked(q):
                p = q
            else:  # try axis-wise slide
                qx = p + np.array([v[0], 0.0]) * dt / 4
                qy = p + np.array([0.0, v[1]]) * dt / 4
                if not self.blocked(qx):
                    p = qx
                elif not self.blocked(qy):
                    p = qy
        return p

    # A* over cells (dataset generation + oracle waypoints)
    def astar(self, start_rc, goal_rc):
        def h(a, b):
            return abs(a[0] - b[0]) + abs(a[1] - b[1])
        openq = [(h(start_rc, goal_rc), 0, start_rc, None)]
        came, costs = {}, {start_rc: 0}
        while openq:
            _, g, cur, par = heapq.heappop(openq)
            if cur in came:
                continue
            came[cur] = par
            if cur == goal_rc:
                path = [cur]
                while came[path[-1]] is not None:
                    path.append(came[path[-1]])
                return path[::-1]
            for dr, dc in ((0, 1), (0, -1), (1, 0), (-1, 0)):
                nxt = (cur[0] + dr, cur[1] + dc)
                if self.blocked_cell(*nxt) or nxt in came:
                    continue
                ng = g + 1
                if ng < costs.get(nxt, 1e9):
                    costs[nxt] = ng
                    heapq.heappush(openq, (ng + h(nxt, goal_rc), ng, nxt, cur))
        return None


def traj_pairs(trajs, n_pairs, rng, max_gap=200):
    """Sample (s_i, s_{i+k}) within trajectories: d(s_i, s_{i+k}) <= k (time-to-reach upper bound)."""
    A, B, K = [], [], []
    for _ in range(n_pairs):
        tr = trajs[rng.integers(len(trajs))]
        if len(tr) < 3:
            continue
        i = rng.integers(0, len(tr) - 2)
        j = rng.integers(i + 1, min(len(tr), i + max_gap))
        A.append(tr[i]); B.append(tr[j]); K.append(j - i)
    return (np.array(A, dtype=np.float32), np.array(B, dtype=np.float32),
            np.array(K, dtype=np.float32))


def make_dataset(maze, n_traj=500, seed=0, noise=0.05):
    """Offline dataset: noisy waypoint-following trajectories between random cells."""
    rng = np.random.default_rng(seed)
    cells = maze.free_cells()
    obs, nxt = [], []
    trajs = []
    for _ in range(n_traj):
        a, b = rng.choice(len(cells), 2, replace=False)
        path = maze.astar(cells[a], cells[b])
        if path is None or len(path) < 2:
            continue
        wps = [maze.cell_center(rc) for rc in path]
        pos = wps[0] + rng.uniform(-0.2, 0.2, 2)
        traj = [pos.copy()]
        wi = 0
        for _ in range(60 * len(wps)):
            tgt = wps[min(wi, len(wps) - 1)]
            if np.linalg.norm(tgt - pos) < 0.3:
                wi += 1
                if wi >= len(wps):
                    break
                continue
            v = tgt - pos
            v = v / (np.linalg.norm(v) + 1e-8) * 0.25 + rng.normal(0, noise, 2)
            newp = maze.step(pos, v)
            obs.append(pos.copy())
            nxt.append(newp.copy())
            pos = newp
            traj.append(pos.copy())
        trajs.append(np.array(traj))
    return np.array(obs, dtype=np.float32), np.array(nxt, dtype=np.float32), trajs


# ---------------------------------------------------------------- IQE quasimetric
class IQE(nn.Module):
    """Interval Quasimetric Embedding (Wang & Isola 2022), maxmean reduction."""

    def __init__(self, in_dim=2, latent=64, groups=8, hidden=256):
        super().__init__()
        assert latent % groups == 0
        self.groups, self.k = groups, latent // groups
        self.enc = nn.Sequential(
            nn.Linear(in_dim, hidden), nn.ReLU(),
            nn.Linear(hidden, hidden), nn.ReLU(),
            nn.Linear(hidden, latent),
        )
        self.alpha = nn.Parameter(torch.zeros(()))  # maxmean mix
        self.scale = nn.Parameter(torch.zeros(()))

    def dist(self, x, y):
        zx, zy = self.enc(x), self.enc(y)
        zx = zx.view(*zx.shape[:-1], self.groups, self.k)
        zy = zy.view(*zy.shape[:-1], self.groups, self.k)
        # interval length sum per group: components where zy > zx extend the interval
        d = torch.relu(zy - zx).sum(-1)  # (..., groups)
        alpha = torch.sigmoid(self.alpha)
        maxmean = alpha * d.max(-1).values + (1 - alpha) * d.mean(-1)
        return maxmean * torch.exp(self.scale)


def train_quasimetric(obs, nxt, steps=4000, batch=1024, device="cpu", seed=0,
                      margin_target=1.0, verbose=True, trajs=None):
    """QRL-style loss: 1-step transitions have d<=1; within-trajectory pairs give
    multi-step upper bounds d(s_i, s_{i+k}) <= k; random pairs are pushed apart
    under a Lagrangian so distances are maximal subject to consistency."""
    torch.manual_seed(seed)
    rng = np.random.default_rng(seed)
    model = IQE().to(device)
    opt = torch.optim.Adam(model.parameters(), lr=3e-4)
    lam = torch.zeros((), device=device, requires_grad=True)
    opt_lam = torch.optim.Adam([lam], lr=1e-2)
    O = torch.as_tensor(obs, device=device)
    N = torch.as_tensor(nxt, device=device)
    n = len(O)
    if trajs is not None:
        A, B, K = traj_pairs(trajs, 200000, rng)
        A = torch.as_tensor(A, device=device); B = torch.as_tensor(B, device=device)
        K = torch.as_tensor(K, device=device)
        # saturation margin: push non-successor pairs apart only up to ~the
        # longest observed time-to-reach (unbounded pushing inflates distances
        # between rarely co-visited regions and breaks graph edges)
        margin = float(np.quantile(K.cpu().numpy(), 0.95)) * 1.5
    else:
        margin = 200.0
    for it in range(steps):
        i = torch.randint(0, n, (batch,), device=device)
        j = torch.randint(0, n, (batch,), device=device)
        d_loc = model.dist(O[i], N[i])          # should be <= 1 (one step)
        viol = (torch.relu(d_loc - margin_target) ** 2).mean()
        if trajs is not None:
            m = torch.randint(0, len(A), (batch,), device=device)
            d_multi = model.dist(A[m], B[m])
            viol = viol + (torch.relu((d_multi - K[m]) / K[m].clamp(min=1)) ** 2).mean()
        d_glob = model.dist(O[i], O[j])         # push up, saturating at margin
        glob = torch.relu(margin - d_glob).mean() / margin
        loss = glob + torch.exp(lam.detach()) * viol
        opt.zero_grad(); loss.backward(); opt.step()
        lam_loss = -torch.exp(lam) * (viol.detach() - 0.05)
        opt_lam.zero_grad(); lam_loss.backward(); opt_lam.step()
        if verbose and (it + 1) % 1000 == 0:
            print(f"  [qm] step {it+1}: viol={viol.item():.4f} "
                  f"E[d_glob]={d_glob.mean().item():.2f} lam={lam.item():.2f}")
    return model


@torch.no_grad()
def qdist(model, X, Y, device="cpu", bs=4096):
    """Pairwise quasimetric d(X_i, Y_j) -> (len(X), len(Y)) matrix."""
    X = torch.as_tensor(X, dtype=torch.float32, device=device)
    Y = torch.as_tensor(Y, dtype=torch.float32, device=device)
    out = torch.empty(len(X), len(Y))
    for a in range(0, len(X), 256):
        xa = X[a:a + 256].unsqueeze(1).expand(-1, len(Y), -1)
        out[a:a + 256] = model.dist(xa, Y.unsqueeze(0).expand(xa.shape[0], -1, -1)).cpu()
    return out.numpy()


# ---------------------------------------------------------------- Claim 2: greedy dominating set
def greedy_dominating_set(D_sym, tau):
    """Greedy set-cover approximation of the dominating set of the tau-ball graph.

    D_sym: (n, n) symmetrized quasimetric among candidate states.
    Returns (keypoint indices, cover time, n_uncovered)."""
    n = len(D_sym)
    covered = np.zeros(n, dtype=bool)
    cover_mask = D_sym <= tau  # cover_mask[i, j]: i covers j
    keypoints = []
    t0 = time.time()
    gain = cover_mask.sum(1).astype(np.int64)
    while not covered.all():
        i = int(np.argmax(gain))
        if gain[i] <= 0:
            break  # disconnected leftovers
        newly = cover_mask[i] & ~covered
        keypoints.append(i)
        covered |= cover_mask[i]
        gain = (cover_mask & ~covered[None, :]).sum(1)
        gain[keypoints] = -1
    return keypoints, time.time() - t0, int((~covered).sum())


def ilp_dominating_set_lb(D_sym, tau, time_limit=10):
    """LP relaxation lower bound of dominating set size (for approximation-quality check)."""
    try:
        from scipy.optimize import linprog
    except ImportError:
        return None
    n = len(D_sym)
    A = -(D_sym <= tau).astype(float).T   # each state j: sum_i x_i [i covers j] >= 1
    res = linprog(c=np.ones(n), A_ub=A, b_ub=-np.ones(n), bounds=[(0, 1)] * n,
                  method="highs")
    return res.fun if res.success else None


# ---------------------------------------------------------------- graph + planning
class AQMGraph:
    def __init__(self, keypoints_xy, D_kk, edge_thresh, knn=4):
        self.kp = keypoints_xy
        self.D = D_kk
        n = len(keypoints_xy)
        keep = np.zeros((n, n), dtype=bool)
        for i in range(n):
            order = np.argsort(D_kk[i])
            for j in order[1:knn + 1]:
                keep[i, int(j)] = keep[int(j), i] = True
            keep[i] |= D_kk[i] <= edge_thresh
        # MST on symmetrized distances guarantees a connected skeleton; edge
        # weights remain the learned quasimetric, so inflated links are used
        # only when no shorter route exists.
        Ds = np.maximum(D_kk, D_kk.T)
        in_tree = [0]
        best = Ds[0].copy(); best_from = np.zeros(n, dtype=int)
        for _ in range(n - 1):
            best[in_tree] = np.inf
            j = int(np.argmin(best))
            if not np.isfinite(best[j]):
                break
            keep[best_from[j], j] = keep[j, best_from[j]] = True
            in_tree.append(j)
            upd = Ds[j] < best
            best[upd] = Ds[j][upd]; best_from[upd] = j
        self.edges = {i: [(j, D_kk[i, j]) for j in range(n) if j != i and keep[i, j]]
                      for i in range(n)}
        self.pruned = set()

    def n_edges(self):
        return sum(len(v) for v in self.edges.values())

    def dijkstra(self, src, dst):
        dist = {src: 0.0}
        par = {}
        pq = [(0.0, src)]
        while pq:
            d, u = heapq.heappop(pq)
            if u == dst:
                break
            if d > dist.get(u, 1e18):
                continue
            for v, w in self.edges[u]:
                if (u, v) in self.pruned:
                    continue
                nd = d + w
                if nd < dist.get(v, 1e18):
                    dist[v] = nd
                    par[v] = u
                    heapq.heappush(pq, (nd, v))
        if dst not in par and dst != src:
            return None
        path = [dst]
        while path[-1] != src:
            path.append(par[path[-1]])
        return path[::-1]


def navigate(maze, graph, model, start, goal, device="cpu", max_steps=2000,
             replan=False, budget_beta=3.0, goal_radius=0.5, waypoint_radius=0.35):
    """Follow keypoint plan with oracle local controller.
    replan=True: prune current edge if time-on-edge exceeds beta * d_q(edge) and replan."""
    def nearest_kp(x, to=False):
        d = qdist(model, graph.kp, x[None], device=device)[:, 0] if to else \
            qdist(model, x[None], graph.kp, device=device)[0]
        return int(np.argmin(d)), float(np.min(d))

    def local_step(pos, tgt, horizon=6):
        """Bounded-horizon local policy emulator (shared by ALL methods): a competent
        goal-conditioned policy can reach nearby targets around local geometry, but
        has no global knowledge. If the target needs a detour longer than `horizon`
        cells, the policy makes no progress (returns straight-push attempt)."""
        cur_rc = (int(pos[1]), int(pos[0]))
        tgt_rc = (int(tgt[1]), int(tgt[0]))
        if cur_rc != tgt_rc:
            p = maze.astar(cur_rc, tgt_rc)
            if p is not None and len(p) - 1 <= horizon:
                sub = maze.cell_center(p[1]) if len(p) > 1 else tgt
                # steer to next cell center, or directly if same cell
                aim = tgt if len(p) <= 2 else sub
                v = aim - pos
                return v / (np.linalg.norm(v) + 1e-8) * 0.25
        # same cell, or unreachable within horizon: push straight (may stall at wall)
        v = tgt - pos
        return v / (np.linalg.norm(v) + 1e-8) * 0.25

    pos = start.copy()
    k_cur, _ = nearest_kp(pos)               # nearest keypoint from current pos
    k_goal, _ = nearest_kp(goal, to=True)    # keypoint nearest to goal (directed)
    path = graph.dijkstra(k_cur, k_goal)
    if path is None:
        return False, 0, 0
    leg = 1 if len(path) > 1 else 0
    t_edge, replans = 0, 0
    for t in range(max_steps):
        if np.linalg.norm(pos - goal) < goal_radius:
            return True, t, replans
        tgt = graph.kp[path[leg]] if leg < len(path) else goal
        if np.linalg.norm(tgt - pos) < waypoint_radius and leg < len(path):
            leg += 1
            t_edge = 0
            continue
        pos = maze.step(pos, local_step(pos, tgt))
        t_edge += 1
        if replan and leg < len(path) and leg >= 1:
            d_edge = graph.D[path[leg - 1], path[leg]]
            if t_edge > budget_beta * max(d_edge, 4.0):
                graph.pruned.add((path[leg - 1], path[leg]))
                replans += 1
                k_here, _ = nearest_kp(pos)
                path = graph.dijkstra(k_here, k_goal)
                if path is None:
                    return False, t, replans
                leg = 1 if len(path) > 1 else 0
                t_edge = 0
    return False, max_steps, replans


# ---------------------------------------------------------------- dense baseline (SoRB-style)
class DenseGraph(AQMGraph):
    """One node per (subsampled) dataset state — prior graph-based approach scale."""
    pass