""" Robot Policy Evaluation Harness Interactive HuggingFace Space — Bayesian + SPARC + STL on real robot data. Based on: Kress-Gazit et al. (TRI/Cornell) arXiv:2409.09491 """ import numpy as np import pandas as pd import plotly.graph_objects as go import plotly.express as px from plotly.subplots import make_subplots from scipy.fft import rfft, rfftfreq from scipy import stats from datasets import load_dataset import gradio as gr import io, json # ── constants ──────────────────────────────────────────────────────────────── PALETTE = ["#60A5FA", "#FB923C", "#F87171", "#34D399", "#A78BFA"] BG = "#0F172A" CARD = "#1E293B" BORDER = "#334155" TEXT = "#F1F5F9" SUBTEXT = "#94A3B8" ACCENT = "#38BDF8" PLOTLY_LAYOUT = dict( paper_bgcolor=CARD, plot_bgcolor=CARD, font=dict(color=TEXT, family="Inter, sans-serif"), margin=dict(l=40, r=20, t=50, b=40), legend=dict(bgcolor="rgba(0,0,0,0)", bordercolor=BORDER), xaxis=dict(gridcolor=BORDER, zerolinecolor=BORDER), yaxis=dict(gridcolor=BORDER, zerolinecolor=BORDER), ) FS = 50 # Hz — ALOHA dataset sampling rate # ── signal extraction ───────────────────────────────────────────────────────── def extract_episode(states, actions): states = np.array(states, dtype=float) actions = np.array(actions, dtype=float) dq = np.diff(states, axis=0) speed = np.linalg.norm(dq, axis=1) * FS # align dims before subtracting — state and action may differ (e.g. Franka 13 vs 15) min_dim = min(states.shape[1], actions.shape[1]) effort = np.linalg.norm(actions[:, :min_dim] - states[:, :min_dim], axis=1) raw_z = states[:, 1] z = (raw_z - raw_z.min()) / (raw_z.max() - raw_z.min() + 1e-9) return speed, effort, z # ── SPARC ───────────────────────────────────────────────────────────────────── def sparc(speed, fs=FS, padlevel=4, fc=10.0, amp_th=0.05): speed = np.asarray(speed, dtype=float) if speed.max() == 0: return 0.0 nfft = int(pow(2, np.ceil(np.log2(len(speed))) + padlevel)) freqs = rfftfreq(nfft, d=1.0 / fs) Mf = np.abs(rfft(speed, n=nfft)); Mf /= Mf.max() inx = np.where((freqs <= fc) & (Mf >= amp_th))[0] fc_used = freqs[inx[-1]] if len(inx) else fc inx = np.where(freqs <= fc_used)[0] dMf = np.diff(Mf[inx]) / (freqs[1] - freqs[0]) _trapz = getattr(np, "trapezoid", None) or getattr(np, "trapz") return float(-np.sqrt(_trapz(dMf**2 + 1, freqs[inx[:-1]]))) # ── STL manual robustness ───────────────────────────────────────────────────── def stl_robustness(effort, z, threshold): """min over t of: if effort>threshold then z>0.3""" high = effort > threshold if high.any(): return float((z[high] - 0.3).min()) return float((threshold - effort).min()) # ── Bayesian helpers ────────────────────────────────────────────────────────── def posterior(s, n, N=200_000): return np.random.beta(1 + s, 1 + n - s, N) def ci_lower(s, n, N=100_000): return float(np.percentile(np.random.beta(1 + s, 1 + n - s, N), 5)) # ── load ALOHA demo data ────────────────────────────────────────────────────── _cache = {} def load_aloha(): if "aloha" in _cache: return _cache["aloha"] raw = load_dataset("lerobot/aloha_static_cups_open", split="train") episodes = {} for row in raw: ei = row["episode_index"] if ei not in episodes: episodes[ei] = {"states": [], "actions": []} episodes[ei]["states"].append(row["observation.state"]) episodes[ei]["actions"].append(row["action"]) ep_ids = sorted(episodes.keys()) extracted = {} for ei in ep_ids: speed, effort, z = extract_episode(episodes[ei]["states"], episodes[ei]["actions"]) extracted[ei] = {"speed": speed, "effort": effort, "z": z} _cache["aloha"] = (ep_ids, extracted) return ep_ids, extracted # ── core analysis ───────────────────────────────────────────────────────────── def run_analysis(policy_data): """ policy_data: dict of name → {trials, speeds, efforts, zs} Returns dict of figures + report text. """ names = list(policy_data.keys()) colors = {n: PALETTE[i] for i, n in enumerate(names)} all_efforts = np.concatenate([e for d in policy_data.values() for e in d["efforts"]]) effort_thresh = float(np.percentile(all_efforts, 75)) # ── compute metrics ─────────────────────────────────────────────────────── metrics = {} for name, d in policy_data.items(): s = sum(d["trials"]); n = len(d["trials"]) sc = [sparc(sp) for sp in d["speeds"]] st = [stl_robustness(ef, z, effort_thresh) for ef, z in zip(d["efforts"], d["zs"])] metrics[name] = { "s": s, "n": n, "sparc": sc, "stl": st, "ci_lo": ci_lower(s, n), "safe": sum(1 for x in st if x >= 0) / len(st), } # ── fig 1: bayesian posteriors ──────────────────────────────────────────── x = np.linspace(0, 1, 400) fig1 = go.Figure() for name in names: m = metrics[name] a, b = 1 + m["s"], 1 + m["n"] - m["s"] y = stats.beta.pdf(x, a, b) fig1.add_trace(go.Scatter( x=x, y=y, mode="lines", name=f"Policy {name} ({m['s']}/{m['n']})", line=dict(color=colors[name], width=2.5), fill="tozeroy", fillcolor=colors[name].replace(")", ",0.1)").replace("rgb", "rgba"), )) fig1.add_vline(x=m["ci_lo"], line_color=colors[name], line_dash="dot", line_width=1.5) fig1.update_layout(**PLOTLY_LAYOUT, title="① Bayesian Posteriors (dotted = 95 % CI lower bound)", xaxis_title="Success probability p", yaxis_title="Density") # pairwise matrix mat = np.zeros((len(names), len(names))) samps = {n: posterior(metrics[n]["s"], metrics[n]["n"]) for n in names} for i, a in enumerate(names): for j, b in enumerate(names): mat[i, j] = (samps[a] > samps[b]).mean() fig1b = go.Figure(go.Heatmap( z=mat, x=[f"Policy {n}" for n in names], y=[f"Policy {n}" for n in names], colorscale="RdYlGn", zmin=0, zmax=1, text=[[f"{mat[i,j]:.2f}" for j in range(len(names))] for i in range(len(names))], texttemplate="%{text}", textfont=dict(size=14), )) fig1b.update_layout(**PLOTLY_LAYOUT, title="P(row beats col)") # ── fig 2: SPARC ────────────────────────────────────────────────────────── fig2 = go.Figure() for name in names: sc = metrics[name]["sparc"] fig2.add_trace(go.Box( y=sc, name=f"Policy {name}", marker_color=colors[name], line_color=colors[name], boxmean=True, fillcolor=colors[name].replace(")", ",0.3)").replace("rgb", "rgba"), )) fig2.add_hline(y=np.mean([v for m in metrics.values() for v in m["sparc"]]), line_dash="dot", line_color=SUBTEXT, annotation_text="global mean") fig2.update_layout(**PLOTLY_LAYOUT, title="② SPARC Smoothness (less negative = smoother)", yaxis_title="SPARC score") # sample speed profiles fig2b = go.Figure() for name in names: sp = policy_data[name]["speeds"][0] t = np.arange(len(sp)) / FS fig2b.add_trace(go.Scatter(x=t, y=sp, mode="lines", name=f"Policy {name}", line=dict(color=colors[name], width=1.8))) fig2b.update_layout(**PLOTLY_LAYOUT, title="Joint-Space Speed Profile (first episode per policy)", xaxis_title="Time (s)", yaxis_title="Speed (rad/s)") # ── fig 3: STL ──────────────────────────────────────────────────────────── fig3 = go.Figure() for name in names: st = metrics[name]["stl"] fig3.add_trace(go.Scatter( x=[f"Policy {name}"] * len(st), y=st, mode="markers", name=f"Policy {name}", marker=dict(color=colors[name], size=9, opacity=0.7, line=dict(color="white", width=0.5)), )) fig3.add_trace(go.Scatter( x=[f"Policy {name}", f"Policy {name}"], y=[np.mean(st), np.mean(st)], mode="lines", line=dict(color=colors[name], width=4), showlegend=False, )) fig3.add_hline(y=0, line_dash="dash", line_color="white", line_width=1.5, annotation_text="violation boundary") fig3.update_layout(**PLOTLY_LAYOUT, title="③ STL Safety Robustness (positive = constraint satisfied)", yaxis_title="Robustness score") # violation bar viols = [sum(1 for x in metrics[n]["stl"] if x < 0) for n in names] totals = [metrics[n]["n"] for n in names] fig3b = go.Figure(go.Bar( x=[f"Policy {n}" for n in names], y=viols, marker_color=[colors[n] for n in names], text=[f"{v}/{t}" for v, t in zip(viols, totals)], textposition="outside", )) fig3b.update_layout(**PLOTLY_LAYOUT, title="Constraint Violations per Policy", yaxis_title="# violations") # ── fig 4: composite radar + bar ────────────────────────────────────────── def normalize(vals): lo, hi = min(vals), max(vals) return [(v - lo) / (hi - lo + 1e-9) for v in vals] sparc_norm = normalize([-metrics[n]["ci_lo"] for n in names]) # invert (less neg = better) sparc_norm = [1 - v for v in normalize([-metrics[n]["ci_lo"] for n in names])] sparc_norm = normalize([-np.mean(metrics[n]["sparc"]) for n in names]) sparc_norm = [1 - v for v in sparc_norm] composite = {} for i, name in enumerate(names): m = metrics[name] composite[name] = ( 0.40 * m["ci_lo"] + 0.20 * sparc_norm[i] + 0.25 * m["safe"] + 0.15 * (m["s"] / m["n"]) ) cats = ["Success
(CI lb)", "Smoothness", "Safety
(STL)", "Success
rate"] fig4 = go.Figure() for i, name in enumerate(names): m = metrics[name] vals = [m["ci_lo"], sparc_norm[i], m["safe"], m["s"] / m["n"]] vals += vals[:1] theta = cats + [cats[0]] fig4.add_trace(go.Scatterpolar( r=vals, theta=theta, fill="toself", name=f"Policy {name}", line=dict(color=colors[name], width=2), fillcolor=colors[name].replace(")", ",0.15)").replace("rgb", "rgba"), )) fig4.update_layout( paper_bgcolor=CARD, font=dict(color=TEXT), polar=dict( bgcolor=CARD, radialaxis=dict(visible=True, range=[0, 1], gridcolor=BORDER, color=SUBTEXT), angularaxis=dict(gridcolor=BORDER, color=TEXT), ), title="④ Composite Radar", legend=dict(bgcolor="rgba(0,0,0,0)"), margin=dict(l=60, r=60, t=60, b=40), ) cv = [composite[n] for n in names] fig4b = go.Figure(go.Bar( x=[f"Policy {n}" for n in names], y=cv, marker_color=[colors[n] for n in names], text=[f"{v:.3f}" for v in cv], textposition="outside", )) winner = names[int(np.argmax(cv))] fig4b.update_layout(**PLOTLY_LAYOUT, title=f"④ Final Ranking (winner: Policy {winner})", yaxis_title="Composite score", yaxis_range=[0, max(cv) * 1.3]) # ── scorecard text ──────────────────────────────────────────────────────── rows = ["| Metric | " + " | ".join(f"Policy {n}" for n in names) + " |", "|" + "---|" * (len(names) + 1)] defs = [ ("Episodes", lambda n: str(metrics[n]["n"])), ("Successes", lambda n: f"{metrics[n]['s']}/{metrics[n]['n']} ({metrics[n]['s']/metrics[n]['n']:.0%})"), ("95% CI lower", lambda n: f"{metrics[n]['ci_lo']:.1%}"), ("Mean SPARC", lambda n: f"{np.mean(metrics[n]['sparc']):.3f}"), ("Safe fraction", lambda n: f"{metrics[n]['safe']:.0%}"), ("Composite", lambda n: f"**{composite[n]:.3f}**"), ] for label, fn in defs: rows.append("| " + label + " | " + " | ".join(fn(n) for n in names) + " |") rows.append(f"\n🏆 **Recommended policy: {winner}**") rows.append(f"\nEffort threshold used for STL: `{effort_thresh:.4f}`") return fig1, fig1b, fig2, fig2b, fig3, fig3b, fig4, fig4b, "\n".join(rows) # ── demo analysis (ALOHA) ───────────────────────────────────────────────────── def run_demo(n_A, n_B, n_C, sr_A, sr_B, sr_C, progress=gr.Progress()): progress(0, desc="Loading ALOHA dataset from HuggingFace…") ep_ids, extracted = load_aloha() total = n_A + n_B + n_C if total > len(ep_ids): n_A = min(n_A, len(ep_ids) // 3) n_B = min(n_B, len(ep_ids) // 3) n_C = len(ep_ids) - n_A - n_B progress(0.3, desc="Extracting signals…") ids_A = ep_ids[:n_A] ids_B = ep_ids[n_A:n_A + n_B] ids_C = ep_ids[n_A + n_B:n_A + n_B + n_C] def make_policy(eids, sr): n = len(eids) ns = int(round(sr * n)) t = [1]*ns + [0]*(n - ns); np.random.shuffle(t) return { "trials": t, "speeds": [extracted[ei]["speed"] for ei in eids], "efforts": [extracted[ei]["effort"] for ei in eids], "zs": [extracted[ei]["z"] for ei in eids], } policy_data = { "A": make_policy(ids_A, sr_A / 100), "B": make_policy(ids_B, sr_B / 100), "C": make_policy(ids_C, sr_C / 100), } progress(0.6, desc="Running Bayesian + SPARC + STL analysis…") results = run_analysis(policy_data) progress(1.0, desc="Done!") return results # ── upload analysis ──────────────────────────────────────────────────────────── def run_upload(file): if file is None: return [None]*8 + ["⚠️ Please upload a CSV file."] df = pd.read_csv(file.name) required = {"episode_id", "success"} state_cols = [c for c in df.columns if c.startswith("state_")] action_cols = [c for c in df.columns if c.startswith("action_")] if not required.issubset(df.columns): return [None]*8 + [f"⚠️ CSV must have columns: episode_id, success, state_0…state_N, action_0…action_N\nFound: {list(df.columns)}"] if not state_cols: return [None]*8 + ["⚠️ No state columns found (expected state_0, state_1, …)"] # Group by episode policy_data = {"A": {"trials": [], "speeds": [], "efforts": [], "zs": []}} for ei, grp in df.groupby("episode_id"): states = grp[state_cols].values actions = grp[action_cols].values if action_cols else states speed, effort, z = extract_episode(states, actions) policy_data["A"]["trials"].append(int(grp["success"].iloc[-1])) policy_data["A"]["speeds"].append(speed) policy_data["A"]["efforts"].append(effort) policy_data["A"]["zs"].append(z) # If policy_name column exists, split into multiple policies if "policy_name" in df.columns: policy_data = {} for pname, pdf in df.groupby("policy_name"): pd_ = {"trials": [], "speeds": [], "efforts": [], "zs": []} for ei, grp in pdf.groupby("episode_id"): states = grp[state_cols].values actions = grp[action_cols].values if action_cols else states speed, effort, z = extract_episode(states, actions) pd_["trials"].append(int(grp["success"].iloc[-1])) pd_["speeds"].append(speed) pd_["efforts"].append(effort) pd_["zs"].append(z) policy_data[str(pname)] = pd_ return run_analysis(policy_data) # ── CSV template + sample downloads ─────────────────────────────────────────── def make_template(): rows = [] for ep in range(3): for frame in range(20): row = {"episode_id": ep, "policy_name": ["A","B","C"][ep], "success": int(frame == 19)} for i in range(7): row[f"state_{i}"] = round(np.random.randn() * 0.5, 4) row[f"action_{i}"] = round(np.random.randn() * 0.5, 4) rows.append(row) df = pd.DataFrame(rows) path = "/tmp/robot_eval_template.csv" df.to_csv(path, index=False) return path SAMPLE_DATASETS = { "ALOHA bimanual — cup opening (14-DOF)": ("lerobot/aloha_static_cups_open", "observation.state", "action", 20), "Push-T real robot — tabletop push (8-DOF)": ("lerobot/columbia_cairlab_pusht_real", "observation.state", "action", 20), "Franka Panda — free-play manipulation (13-DOF)": ("lerobot/nyu_franka_play_dataset", "observation.state", "action", 20), "Unitree H1 humanoid — warehouse (19-DOF / 40-DOF action)": ("lerobot/unitreeh1_warehouse", "observation.state", "action", 12), } def download_sample(choice, progress=gr.Progress()): if not choice: return None progress(0.1, desc=f"Loading {choice}…") hf, sc, ac, max_eps = SAMPLE_DATASETS[choice] ds = load_dataset(hf, split="train") df_raw = ds.to_pandas() ep_ids = sorted(df_raw["episode_index"].unique())[:max_eps] rows = [] policy_name = choice.split("—")[0].strip() progress(0.4, desc="Extracting episodes…") for ei in ep_ids: grp = df_raw[df_raw["episode_index"] == ei].reset_index(drop=True) success = int(grp["next.reward"].max() > 0) if "next.reward" in grp.columns else 1 states = np.vstack(grp[sc].values) actions = np.vstack(grp[ac].values) for fi, (s, a) in enumerate(zip(states, actions)): row = {"episode_id": int(ei), "policy_name": policy_name, "frame_id": fi, "success": success} for i, v in enumerate(s): row[f"state_{i}"] = round(float(v), 6) for i, v in enumerate(a): row[f"action_{i}"] = round(float(v), 6) rows.append(row) path = f"/tmp/sample_{hf.split('/')[-1]}.csv" pd.DataFrame(rows).to_csv(path, index=False) progress(1.0, desc="Ready!") return path # ── UI ──────────────────────────────────────────────────────────────────────── CSS = f""" :root {{ --bg: {BG}; --card: {CARD}; --border: {BORDER}; --text: {TEXT}; --sub: {SUBTEXT}; --accent: {ACCENT}; }} body, .gradio-container {{ background: var(--bg) !important; color: var(--text) !important; }} .gr-box, .gr-panel {{ background: var(--card) !important; border-color: var(--border) !important; }} .gr-button-primary {{ background: var(--accent) !important; color: #0F172A !important; font-weight: 700; }} .gr-button {{ border-color: var(--border) !important; color: var(--text) !important; }} footer {{ display: none !important; }} h1, h2, h3 {{ color: var(--text) !important; }} label {{ color: var(--sub) !important; }} .tab-nav button {{ color: var(--sub) !important; }} .tab-nav button.selected {{ color: var(--accent) !important; border-color: var(--accent) !important; }} """ HEADER = """

🤖 Robot Policy Evaluation Harness

Bayesian statistics · SPARC smoothness · STL safety constraints

Based on Kress-Gazit et al. (TRI/Cornell) · arXiv:2409.09491

""" FORMAT_HINT = """ **Expected CSV format:** ``` episode_id, policy_name, success, state_0, state_1, ..., state_N, action_0, action_1, ..., action_N 0, A, 0, -0.001, -0.963, 1.173, ... 0, A, 0, -0.013, -0.952, 1.168, ... ... 0, A, 1, ... ← last frame: success=1 1, B, 0, ... ``` - `episode_id`: integer, groups frames into one rollout - `policy_name`: string, used to group into comparison groups (omit for single-policy) - `success`: 0 or 1 (use the value on the **last frame** of the episode) - `state_N`: joint position at each timestep (any number of joints) - `action_N`: commanded joint position (optional — if absent, effort will be zero) """ def build_ui(): with gr.Blocks(css=CSS, title="Robot Policy Eval Harness") as demo: gr.HTML(HEADER) with gr.Tabs(): # ── TAB 1: DEMO DATA ────────────────────────────────────────────── with gr.Tab("🦾 Try with Real ALOHA Data"): gr.Markdown(""" **Dataset**: [`lerobot/aloha_static_cups_open`](https://huggingface.co/datasets/lerobot/aloha_static_cups_open) — 50 real episodes of a bimanual ALOHA robot opening a cup lid, collected via human teleoperation. Adjust the sliders to configure policies, then run the analysis. """) with gr.Row(): with gr.Column(scale=1): gr.Markdown("#### Policy A") n_A = gr.Slider(5, 20, value=15, step=1, label="Episodes") sr_A = gr.Slider(10, 100, value=80, step=5, label="Success rate (%)") with gr.Column(scale=1): gr.Markdown("#### Policy B") n_B = gr.Slider(5, 20, value=15, step=1, label="Episodes") sr_B = gr.Slider(10, 100, value=60, step=5, label="Success rate (%)") with gr.Column(scale=1): gr.Markdown("#### Policy C") n_C = gr.Slider(3, 10, value=10, step=1, label="Episodes") sr_C = gr.Slider(10, 100, value=40, step=5, label="Success rate (%)") run_btn = gr.Button("▶ Run Analysis", variant="primary", size="lg") with gr.Row(): fig_bayes = gr.Plot(label="Bayesian Posteriors") fig_bayes_mat = gr.Plot(label="P(row beats col)") with gr.Row(): fig_sparc = gr.Plot(label="SPARC Smoothness") fig_speed = gr.Plot(label="Speed Profiles") with gr.Row(): fig_stl = gr.Plot(label="STL Robustness") fig_viols = gr.Plot(label="Violations") with gr.Row(): fig_radar = gr.Plot(label="Composite Radar") fig_rank = gr.Plot(label="Final Ranking") scorecard = gr.Markdown(label="Scorecard") run_btn.click( fn=run_demo, inputs=[n_A, n_B, n_C, sr_A, sr_B, sr_C], outputs=[fig_bayes, fig_bayes_mat, fig_sparc, fig_speed, fig_stl, fig_viols, fig_radar, fig_rank, scorecard], ) # ── TAB 2: UPLOAD ───────────────────────────────────────────────── with gr.Tab("📂 Upload Your Own Data"): gr.Markdown("### Try a real dataset — or upload your own rollouts") with gr.Row(): with gr.Column(scale=2): gr.Markdown(""" **Step 1 — pick a real robot dataset to download as a ready-to-use CSV:** | Dataset | Robot | DOF | Task | |---|---|---|---| | ALOHA bimanual | Stanford ALOHA (2× ViperX) | 14 | Cup opening | | Push-T real | Columbia delta robot | 8 | Push block to goal | | Franka Panda | NYU Franka Emika Panda | 13 | Free-play manipulation | | Unitree H1 | Full-size humanoid | 19 state / 40 action | Warehouse pick-place | Then upload the downloaded CSV below and hit **Analyse**. """) with gr.Column(scale=1): sample_picker = gr.Dropdown( choices=list(SAMPLE_DATASETS.keys()), label="Real robot dataset", value=None, ) dl_btn = gr.Button("⬇ Download as CSV", variant="secondary") dl_file = gr.File(label="Downloaded CSV (upload below ↓)") dl_btn.click(fn=download_sample, inputs=[sample_picker], outputs=[dl_file]) gr.Markdown("---") tmpl_btn = gr.Button("⬇ Blank template CSV", variant="secondary") tmpl_file = gr.File(label="Template") tmpl_btn.click(fn=make_template, outputs=tmpl_file) with gr.Accordion("CSV format reference", open=False): gr.Markdown(FORMAT_HINT) upload = gr.File(label="⬆ Upload rollout CSV (your own or downloaded above)", file_types=[".csv"]) run_upload_btn = gr.Button("▶ Analyse Uploaded Data", variant="primary", size="lg") with gr.Row(): uf_bayes = gr.Plot(label="Bayesian Posteriors") uf_bayes_mat = gr.Plot(label="P(row beats col)") with gr.Row(): uf_sparc = gr.Plot(label="SPARC Smoothness") uf_speed = gr.Plot(label="Speed Profiles") with gr.Row(): uf_stl = gr.Plot(label="STL Robustness") uf_viols = gr.Plot(label="Violations") with gr.Row(): uf_radar = gr.Plot(label="Composite Radar") uf_rank = gr.Plot(label="Final Ranking") uf_scorecard = gr.Markdown(label="Scorecard") run_upload_btn.click( fn=run_upload, inputs=[upload], outputs=[uf_bayes, uf_bayes_mat, uf_sparc, uf_speed, uf_stl, uf_viols, uf_radar, uf_rank, uf_scorecard], ) # ── TAB 3: ABOUT ────────────────────────────────────────────────── with gr.Tab("📖 About"): gr.Markdown(""" ## What this is A lightweight evaluation harness for robot manipulation policies, based on best practices from [Kress-Gazit et al. (TRI / Cornell), arXiv:2409.09491](https://arxiv.org/abs/2409.09491). The field almost universally reports bare success rate from a handful of trials with no statistical analysis. This tool replaces that with three complementary methods: --- ### ① Bayesian Bernoulli Analysis Models each policy's success probability as a **Beta distribution** rather than a point estimate. Shows the full posterior, 95% credible interval lower bound, and the probability that one policy is genuinely better than another — not just luckier. > *"P(A > B) = 0.83" is very different from "A scored 80%, B scored 60%".* ### ② SPARC Smoothness Computes the **SPectral ARC length** of the robot's joint-space speed profile. Two policies can have identical success rates but completely different motion quality. A policy that succeeds jerkily is unsafe near people and hard on hardware. ### ③ STL Safety Constraints Encodes behavioral requirements as **Signal Temporal Logic** formulas and automatically scores every rollout — no human video review required. > Example: *"Whenever the robot is straining (high tracking error), the arm must stay above table height."* --- ### Uploading your own data Any robot with joint-position logging works. The CSV format is: ``` episode_id, policy_name, success, state_0 … state_N, action_0 … action_N ``` --- ### Citation ```bibtex @article{kressgazit2024robot, title = {Robot Learning as an Empirical Science}, author = {Kress-Gazit, Hadas and others}, journal = {arXiv preprint arXiv:2409.09491}, year = {2024} } ``` """) return demo if __name__ == "__main__": build_ui().launch()