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Reward Hacking Detector

Detect agents that game proxy metrics without achieving the true intended objective — specification gaming, Goodhart drift, and metric inflation.

Goodhart's Law in Action

"When a measure becomes a target, it ceases to be a good measure." Agents optimising for the letter of the specification rather than its spirit can appear to perform well while being fundamentally misaligned.

Detection Strategies

Pattern Description
Metric–Objective Divergence Proxy metric improving while ground-truth objective stagnates or degrades
Edge-Case Exploitation Agent repeatedly targets boundary conditions or known scoring loopholes
Reward Inflation Reward growing faster than any plausible capability improvement
Goodhart Drift Metric correlation with true objective decreasing over time
Distribution Shift Gaming Agent steering inputs toward distributions where it scores well
Multi-Metric Inconsistency One metric improving while correlated metrics stagnate

Quick Start

from replication.reward_hacking import (
    RewardHackingDetector,
    MetricObservation,
    DetectorConfig,
)

detector = RewardHackingDetector()

# Add observations with both proxy metric and ground truth
for step in range(100):
    detector.add_observation(MetricObservation(
        agent_id="agent-1",
        metric_name="accuracy",
        metric_value=0.5 + step * 0.005,       # proxy keeps improving
        ground_truth=0.5 + step * 0.001,        # ground truth lags
        timestamp=float(step),
    ))

report = detector.analyze()
print(detector.render_text(report))

Custom Configuration

config = DetectorConfig(
    divergence_threshold=0.2,
    inflation_z=2.5,
    goodhart_window=20,
    min_observations=10,
)
detector = RewardHackingDetector(config=config)

CLI Usage

# Default demonstration
python -m replication reward-hacking

# Simulate 5 agents
python -m replication reward-hacking --agents 5

# Preset fleet profiles
python -m replication reward-hacking --preset subtle    # subtle gaming
python -m replication reward-hacking --preset blatant   # obvious gaming
python -m replication reward-hacking --preset clean     # honest baseline
python -m replication reward-hacking --preset mixed     # fleet mix

# Live watch mode
python -m replication reward-hacking --watch --interval 5

# Export
python -m replication reward-hacking -o report.html
python -m replication reward-hacking --json

Core Types

MetricObservation

A single metric reading with optional ground-truth reference.

Field Type Description
agent_id str Agent identifier
metric_name str Name of the proxy metric
metric_value float Observed proxy metric value
ground_truth float \| None True objective value (optional)
timestamp float Unix timestamp

HackingSignal

A single detected reward-hacking signal.

Field Type Description
pattern HackingPattern Which hacking pattern was detected
severity Severity LOW, MEDIUM, HIGH, or CRITICAL
detail str Human-readable description
evidence dict Supporting numerical evidence

RewardHackingReport

Full analysis report. Rendered via render_text(), render_html(), or render_json().

DetectorConfig

Tune detection sensitivity.

Parameter Default Description
divergence_threshold Min gap between proxy and ground-truth to flag
inflation_z Z-score threshold for reward inflation detection
goodhart_window Window size for correlation drift analysis
min_observations Minimum observations before analysis fires

API Reference

RewardHackingDetector

Core reward-hacking detector.

Source code in src/replication/reward_hacking.py
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class RewardHackingDetector:
    """Core reward-hacking detector."""

    def __init__(self, config: Optional[DetectorConfig] = None) -> None:
        self.config = config or DetectorConfig()
        self._profiles: Dict[str, AgentMetricProfile] = {}

    # -- ingestion --

    def add_observation(self, obs: MetricObservation) -> None:
        if obs.agent_id not in self._profiles:
            self._profiles[obs.agent_id] = AgentMetricProfile(obs.agent_id)
        self._profiles[obs.agent_id].add(obs)

    # -- analysis --

    def analyze(self, agent_id: Optional[str] = None) -> RewardHackingReport:
        targets = (
            {agent_id: self._profiles[agent_id]}
            if agent_id and agent_id in self._profiles
            else dict(self._profiles)
        )
        signals: List[HackingSignal] = []
        for aid, prof in targets.items():
            signals.extend(self._detect_divergence(prof))
            signals.extend(self._detect_edge_case(prof))
            signals.extend(self._detect_inflation(prof))
            signals.extend(self._detect_goodhart(prof))
            signals.extend(self._detect_distribution_shift(prof))
            signals.extend(self._detect_inconsistency(prof))
            # risk score
            agent_sigs = [s for s in signals if s.agent_id == aid]
            prof.risk_score = min(1.0, sum(s.confidence for s in agent_sigs) / max(len(agent_sigs), 1) + 0.1 * len(agent_sigs)) if agent_sigs else 0.0

        report = RewardHackingReport(
            profiles=targets,
            signals=sorted(signals, key=lambda s: s.confidence, reverse=True),
            summary=self._build_summary(targets, signals),
            recommendations=self._build_recommendations(signals),
            generated_at=datetime.now(timezone.utc).isoformat(),
        )
        return report

    def analyze_fleet(self) -> RewardHackingReport:
        return self.analyze()

    # -- detection strategies --

    def _eligible_metrics(
        self, prof: AgentMetricProfile, *, require_gt: bool = False,
    ) -> "List[tuple[str, List[float], List[float]]]":
        """Return metrics meeting min-observation threshold.

        Yields ``(name, vals, gt_vals)`` tuples.  When *require_gt* is True
        only metrics with sufficient ground-truth observations are included.
        Centralises the repeated eligibility check used by all six detectors.
        """
        cfg = self.config
        result: "List[tuple[str, List[float], List[float]]]" = []
        for name in prof.metric_names():
            vals = prof.metric_values(name)
            if len(vals) < cfg.min_observations:
                continue
            gts = prof.ground_truths(name)
            gt_vals = [g for g in gts if g is not None]
            if require_gt and len(gt_vals) < cfg.min_observations:
                continue
            result.append((name, vals, gt_vals))
        return result

    def _detect_divergence(self, prof: AgentMetricProfile) -> List[HackingSignal]:
        signals: List[HackingSignal] = []
        cfg = self.config
        for name, vals, gt_vals in self._eligible_metrics(prof, require_gt=True):
            w = min(cfg.window_size, len(vals))
            metric_trend = stats_mean(vals[-w:]) - stats_mean(vals[:w])
            gt_trend = stats_mean(gt_vals[-w:]) - stats_mean(gt_vals[:w])
            gap = metric_trend - gt_trend
            if gap > cfg.divergence_threshold:
                sev = Severity.CRITICAL if gap > 0.6 else Severity.HIGH if gap > 0.4 else Severity.MEDIUM
                conf = min(1.0, gap / 0.8)
                signals.append(HackingSignal(
                    pattern=HackingPattern.METRIC_OBJECTIVE_DIVERGENCE,
                    agent_id=prof.agent_id, severity=sev, confidence=conf,
                    description=f"Metric '{name}' improving by {metric_trend:+.3f} while ground truth moves {gt_trend:+.3f}",
                    evidence={"metric": name, "metric_trend": metric_trend, "gt_trend": gt_trend, "gap": gap},
                ))
        return signals

    def _detect_edge_case(self, prof: AgentMetricProfile) -> List[HackingSignal]:
        signals: List[HackingSignal] = []
        cfg = self.config
        for name, vals, _ in self._eligible_metrics(prof):
            # Count values at exact boundaries (0.0, 1.0, or repeated identical high values)
            boundary_count = sum(1 for v in vals if v >= 0.99 or v <= 0.01)
            repeat_map: Dict[float, int] = defaultdict(int)
            for v in vals:
                repeat_map[round(v, 4)] += 1
            max_repeat = max(repeat_map.values()) if repeat_map else 0
            if boundary_count >= cfg.edge_case_repeat_threshold or max_repeat >= cfg.edge_case_repeat_threshold + 2:
                conf = min(1.0, (boundary_count + max_repeat) / (2 * len(vals)))
                sev = Severity.HIGH if conf > 0.5 else Severity.MEDIUM
                signals.append(HackingSignal(
                    pattern=HackingPattern.EDGE_CASE_EXPLOITATION,
                    agent_id=prof.agent_id, severity=sev, confidence=conf,
                    description=f"Metric '{name}': {boundary_count} boundary values, max repeat {max_repeat}",
                    evidence={"metric": name, "boundary_count": boundary_count, "max_repeat": max_repeat},
                ))
        return signals

    def _detect_inflation(self, prof: AgentMetricProfile) -> List[HackingSignal]:
        signals: List[HackingSignal] = []
        cfg = self.config
        for name, vals, _ in self._eligible_metrics(prof):
            # Compute per-step growth rate
            rates = [(vals[i] - vals[i - 1]) / max(abs(vals[i - 1]), 1e-9) for i in range(1, len(vals))]
            avg_rate = stats_mean(rates)
            if avg_rate > cfg.inflation_rate_threshold:
                conf = min(1.0, avg_rate / (cfg.inflation_rate_threshold * 3))
                sev = Severity.CRITICAL if avg_rate > 0.4 else Severity.HIGH if avg_rate > 0.25 else Severity.MEDIUM
                signals.append(HackingSignal(
                    pattern=HackingPattern.REWARD_INFLATION,
                    agent_id=prof.agent_id, severity=sev, confidence=conf,
                    description=f"Metric '{name}' inflating at avg rate {avg_rate:.3f}/step",
                    evidence={"metric": name, "avg_rate": avg_rate, "rates": rates[-5:]},
                ))
        return signals

    def _detect_goodhart(self, prof: AgentMetricProfile) -> List[HackingSignal]:
        signals: List[HackingSignal] = []
        cfg = self.config
        for name, vals, gt_vals in self._eligible_metrics(prof, require_gt=True):
            n = min(len(vals), len(gt_vals))
            half = n // 2
            if half < 2:
                continue
            early_corr = self._pearson(vals[:half], gt_vals[:half])
            late_corr = self._pearson(vals[half:n], gt_vals[half:n])
            decay = early_corr - late_corr
            if decay > cfg.correlation_decay_threshold:
                conf = min(1.0, decay / 0.8)
                sev = Severity.CRITICAL if decay > 0.6 else Severity.HIGH if decay > 0.4 else Severity.MEDIUM
                signals.append(HackingSignal(
                    pattern=HackingPattern.GOODHART_DRIFT,
                    agent_id=prof.agent_id, severity=sev, confidence=conf,
                    description=f"Metric '{name}' correlation decayed from {early_corr:.3f} to {late_corr:.3f}",
                    evidence={"metric": name, "early_corr": early_corr, "late_corr": late_corr, "decay": decay},
                ))
        return signals

    def _detect_distribution_shift(self, prof: AgentMetricProfile) -> List[HackingSignal]:
        signals: List[HackingSignal] = []
        cfg = self.config
        for name, vals, _ in self._eligible_metrics(prof):
            half = len(vals) // 2
            if half < 2:
                continue
            early_std = stats_std(vals[:half])
            late_std = stats_std(vals[half:])
            # Narrowing distribution while mean rises = gaming
            early_mean = stats_mean(vals[:half])
            late_mean = stats_mean(vals[half:])
            if early_std > 0 and late_std < early_std * 0.5 and late_mean > early_mean:
                ratio = late_std / max(early_std, 1e-9)
                conf = min(1.0, (1.0 - ratio) * 0.8)
                sev = Severity.HIGH if ratio < 0.3 else Severity.MEDIUM
                signals.append(HackingSignal(
                    pattern=HackingPattern.DISTRIBUTION_SHIFT_GAMING,
                    agent_id=prof.agent_id, severity=sev, confidence=conf,
                    description=f"Metric '{name}' distribution narrowing ({early_std:.3f}{late_std:.3f}) while mean rises",
                    evidence={"metric": name, "early_std": early_std, "late_std": late_std,
                              "early_mean": early_mean, "late_mean": late_mean},
                ))
        return signals

    def _detect_inconsistency(self, prof: AgentMetricProfile) -> List[HackingSignal]:
        signals: List[HackingSignal] = []
        cfg = self.config
        eligible = self._eligible_metrics(prof)
        if len(eligible) < 2:
            return signals
        trends: Dict[str, float] = {}
        for name, vals, _ in eligible:
            w = min(cfg.window_size, len(vals))
            trends[name] = stats_mean(vals[-w:]) - stats_mean(vals[:w])
        if len(trends) < 2:
            return signals
        avg_trend = stats_mean(list(trends.values()))
        for name, trend in trends.items():
            gap = abs(trend - avg_trend)
            if gap > cfg.inconsistency_threshold and trend > avg_trend:
                conf = min(1.0, gap / 0.5)
                sev = Severity.HIGH if gap > 0.4 else Severity.MEDIUM
                signals.append(HackingSignal(
                    pattern=HackingPattern.MULTI_METRIC_INCONSISTENCY,
                    agent_id=prof.agent_id, severity=sev, confidence=conf,
                    description=f"Metric '{name}' trend ({trend:+.3f}) diverges from fleet average ({avg_trend:+.3f})",
                    evidence={"metric": name, "trend": trend, "avg_trend": avg_trend, "gap": gap},
                ))
        return signals

    # -- helpers --

    @staticmethod
    def _pearson(xs: List[float], ys: List[float]) -> float:
        n = min(len(xs), len(ys))
        return pearson_correlation(xs[:n], ys[:n])

    def _build_summary(self, profiles: Dict[str, AgentMetricProfile], signals: List[HackingSignal]) -> Dict[str, Any]:
        by_pattern: Dict[str, int] = defaultdict(int)
        by_severity: Dict[str, int] = defaultdict(int)
        for s in signals:
            by_pattern[s.pattern.value] += 1
            by_severity[s.severity.value] += 1
        agents_flagged = len({s.agent_id for s in signals})
        return {
            "total_agents": len(profiles),
            "agents_flagged": agents_flagged,
            "total_signals": len(signals),
            "by_pattern": dict(by_pattern),
            "by_severity": dict(by_severity),
            "avg_confidence": stats_mean([s.confidence for s in signals]) if signals else 0.0,
        }

    def _build_recommendations(self, signals: List[HackingSignal]) -> List[str]:
        recs: List[str] = []
        patterns_seen = {s.pattern for s in signals}
        if HackingPattern.METRIC_OBJECTIVE_DIVERGENCE in patterns_seen:
            recs.append("Add ground-truth validation checkpoints at regular intervals")
            recs.append("Implement dual-metric evaluation pairing proxy with ground truth")
        if HackingPattern.EDGE_CASE_EXPLOITATION in patterns_seen:
            recs.append("Add adversarial evaluation to test for edge-case exploitation")
            recs.append("Randomise evaluation boundaries to prevent targeting")
        if HackingPattern.REWARD_INFLATION in patterns_seen:
            recs.append("Implement reward capping or normalisation to bound growth rates")
            recs.append("Add human-in-the-loop review for suspiciously high scores")
        if HackingPattern.GOODHART_DRIFT in patterns_seen:
            recs.append("Diversify evaluation metrics to prevent single-metric gaming")
            recs.append("Implement metric rotation to prevent adaptation (Goodhart mitigation)")
        if HackingPattern.DISTRIBUTION_SHIFT_GAMING in patterns_seen:
            recs.append("Monitor input distribution statistics alongside output scores")
            recs.append("Enforce evaluation on held-out diverse distribution samples")
        if HackingPattern.MULTI_METRIC_INCONSISTENCY in patterns_seen:
            recs.append("Investigate metrics with divergent trends for possible gaming")
            recs.append("Require correlated improvement across metric families before promotion")
        if not recs:
            recs.append("No reward-hacking signals detected — continue routine monitoring")
        return recs

    # -- rendering --

    def render_text(self, report: RewardHackingReport) -> str:
        lines: List[str] = []
        lines.extend(box_header("REWARD HACKING DETECTOR"))
        lines.append(f"  Generated: {report.generated_at}")
        lines.append(f"  Agents analysed: {report.summary.get('total_agents', 0)}")
        lines.append(f"  Agents flagged:  {report.summary.get('agents_flagged', 0)}")
        lines.append(f"  Total signals:   {report.summary.get('total_signals', 0)}")
        lines.append("")

        if report.signals:
            lines.extend(box_header("SIGNALS"))
            for s in report.signals:
                sev_icon = {"low": "🟢", "medium": "🟡", "high": "🟠", "critical": "🔴"}.get(s.severity.value, "⚪")
                lines.append(f"  {sev_icon} [{s.severity.value.upper():>8}] {s.pattern.value}")
                lines.append(f"    Agent: {s.agent_id}  |  Confidence: {s.confidence:.0%}")
                lines.append(f"    {s.description}")
                lines.append("")

        # Per-agent risk
        lines.extend(box_header("AGENT RISK SCORES"))
        for aid, prof in sorted(report.profiles.items(), key=lambda x: x[1].risk_score, reverse=True):
            bar_len = int(prof.risk_score * 20)
            bar = "█" * bar_len + "░" * (20 - bar_len)
            lines.append(f"  {aid:<20} [{bar}] {prof.risk_score:.0%}")
        lines.append("")

        # Recommendations
        lines.extend(box_header("RECOMMENDATIONS"))
        for i, rec in enumerate(report.recommendations, 1):
            lines.append(f"  {i}. {rec}")
        lines.append("")
        return "\n".join(lines)

    def render_html(self, report: RewardHackingReport) -> str:
        esc = _html.escape

        signal_rows = ""
        for s in report.signals:
            color = {"low": "#4caf50", "medium": "#ff9800", "high": "#f44336", "critical": "#b71c1c"}.get(s.severity.value, "#999")
            signal_rows += f"""<tr>
                <td style="color:{color};font-weight:bold">{esc(s.severity.value.upper())}</td>
                <td>{esc(s.pattern.value)}</td>
                <td>{esc(s.agent_id)}</td>
                <td>{s.confidence:.0%}</td>
                <td>{esc(s.description)}</td>
            </tr>"""

        risk_bars = ""
        for aid, prof in sorted(report.profiles.items(), key=lambda x: x[1].risk_score, reverse=True):
            pct = prof.risk_score * 100
            color = "#4caf50" if pct < 30 else "#ff9800" if pct < 60 else "#f44336"
            risk_bars += f"""<div style="margin:4px 0">
                <span style="display:inline-block;width:140px">{esc(aid)}</span>
                <div style="display:inline-block;width:200px;height:18px;background:#333;border-radius:3px;vertical-align:middle">
                    <div style="width:{pct:.0f}%;height:100%;background:{color};border-radius:3px"></div>
                </div>
                <span style="margin-left:8px">{pct:.0f}%</span>
            </div>"""

        recs_html = "".join(f"<li>{esc(r)}</li>" for r in report.recommendations)

        # Canvas chart data for metric divergence
        chart_js = ""
        for aid, prof in report.profiles.items():
            for name in prof.metric_names():
                vals = prof.metric_values(name)
                gts = [g for g in prof.ground_truths(name) if g is not None]
                if gts:
                    chart_js += f"""
                    drawChart('{esc(aid)}{esc(name)}',
                        {json.dumps(vals[:50])}, {json.dumps(gts[:50])});"""

        return f"""<!DOCTYPE html>
<html lang="en"><head><meta charset="utf-8">
<title>Reward Hacking Report</title>
<style>
body{{font-family:system-ui,sans-serif;background:#1a1a2e;color:#e0e0e0;margin:20px;}}
h1{{color:#e94560;}} h2{{color:#ff9800;border-bottom:1px solid #333;padding-bottom:4px;}}
table{{border-collapse:collapse;width:100%;margin:10px 0;}}
th,td{{border:1px solid #333;padding:6px 10px;text-align:left;}}
th{{background:#16213e;}} tr:nth-child(even){{background:#16213e33;}}
.card{{background:#16213e;border-radius:8px;padding:16px;margin:12px 0;}}
canvas{{background:#0f3460;border-radius:4px;margin:8px;}}
li{{margin:4px 0;}}
</style></head><body>
<h1>🎯 Reward Hacking Detector</h1>
<p>Generated: {esc(report.generated_at)}</p>
<div style="display:flex;gap:16px;flex-wrap:wrap;">
    <div class="card"><h3>Agents</h3><div style="font-size:2em">{report.summary.get('total_agents',0)}</div>analysed</div>
    <div class="card"><h3>Flagged</h3><div style="font-size:2em;color:#f44336">{report.summary.get('agents_flagged',0)}</div>agents</div>
    <div class="card"><h3>Signals</h3><div style="font-size:2em;color:#ff9800">{report.summary.get('total_signals',0)}</div>detected</div>
    <div class="card"><h3>Avg Confidence</h3><div style="font-size:2em">{report.summary.get('avg_confidence',0):.0%}</div></div>
</div>

<h2>Signals</h2>
<table><tr><th>Severity</th><th>Pattern</th><th>Agent</th><th>Confidence</th><th>Description</th></tr>
{signal_rows}</table>

<h2>Agent Risk Scores</h2>
<div class="card">{risk_bars}</div>

<h2>Metric vs Ground Truth</h2>
<div id="charts"></div>

<h2>Recommendations</h2>
<ul>{recs_html}</ul>

<script>
function drawChart(title, metric, gt) {{
    const div = document.getElementById('charts');
    const c = document.createElement('canvas');
    c.width = 400; c.height = 200;
    div.appendChild(c);
    const ctx = c.getContext('2d');
    const n = Math.max(metric.length, gt.length);
    const all = metric.concat(gt);
    const mn = Math.min(...all), mx = Math.max(...all);
    const range = mx - mn || 1;
    ctx.fillStyle = '#e0e0e0'; ctx.font = '11px sans-serif';
    ctx.fillText(title, 8, 14);
    function y(v) {{ return 180 - ((v - mn) / range) * 160; }}
    function x(i) {{ return 10 + (i / Math.max(n - 1, 1)) * 380; }}
    // metric line
    ctx.strokeStyle = '#e94560'; ctx.lineWidth = 2; ctx.beginPath();
    metric.forEach((v, i) => {{ i === 0 ? ctx.moveTo(x(i), y(v)) : ctx.lineTo(x(i), y(v)); }});
    ctx.stroke();
    // gt line
    ctx.strokeStyle = '#4caf50'; ctx.lineWidth = 2; ctx.beginPath();
    gt.forEach((v, i) => {{ i === 0 ? ctx.moveTo(x(i), y(v)) : ctx.lineTo(x(i), y(v)); }});
    ctx.stroke();
    // legend
    ctx.fillStyle = '#e94560'; ctx.fillText('● Metric', 280, 14);
    ctx.fillStyle = '#4caf50'; ctx.fillText('● Ground Truth', 340, 14);
}}
{chart_js}
</script>
</body></html>"""

    def render_json(self, report: RewardHackingReport) -> str:
        return json.dumps({
            "generated_at": report.generated_at,
            "summary": report.summary,
            "signals": [
                {"pattern": s.pattern.value, "agent_id": s.agent_id,
                 "severity": s.severity.value, "confidence": s.confidence,
                 "description": s.description, "evidence": s.evidence}
                for s in report.signals
            ],
            "agent_risks": {aid: prof.risk_score for aid, prof in report.profiles.items()},
            "recommendations": report.recommendations,
        }, indent=2)

__init__(config: Optional[DetectorConfig] = None) -> None

Source code in src/replication/reward_hacking.py
def __init__(self, config: Optional[DetectorConfig] = None) -> None:
    self.config = config or DetectorConfig()
    self._profiles: Dict[str, AgentMetricProfile] = {}

add_observation(obs: MetricObservation) -> None

Source code in src/replication/reward_hacking.py
def add_observation(self, obs: MetricObservation) -> None:
    if obs.agent_id not in self._profiles:
        self._profiles[obs.agent_id] = AgentMetricProfile(obs.agent_id)
    self._profiles[obs.agent_id].add(obs)

analyze(agent_id: Optional[str] = None) -> RewardHackingReport

Source code in src/replication/reward_hacking.py
def analyze(self, agent_id: Optional[str] = None) -> RewardHackingReport:
    targets = (
        {agent_id: self._profiles[agent_id]}
        if agent_id and agent_id in self._profiles
        else dict(self._profiles)
    )
    signals: List[HackingSignal] = []
    for aid, prof in targets.items():
        signals.extend(self._detect_divergence(prof))
        signals.extend(self._detect_edge_case(prof))
        signals.extend(self._detect_inflation(prof))
        signals.extend(self._detect_goodhart(prof))
        signals.extend(self._detect_distribution_shift(prof))
        signals.extend(self._detect_inconsistency(prof))
        # risk score
        agent_sigs = [s for s in signals if s.agent_id == aid]
        prof.risk_score = min(1.0, sum(s.confidence for s in agent_sigs) / max(len(agent_sigs), 1) + 0.1 * len(agent_sigs)) if agent_sigs else 0.0

    report = RewardHackingReport(
        profiles=targets,
        signals=sorted(signals, key=lambda s: s.confidence, reverse=True),
        summary=self._build_summary(targets, signals),
        recommendations=self._build_recommendations(signals),
        generated_at=datetime.now(timezone.utc).isoformat(),
    )
    return report

analyze_fleet() -> RewardHackingReport

Source code in src/replication/reward_hacking.py
def analyze_fleet(self) -> RewardHackingReport:
    return self.analyze()

render_text(report: RewardHackingReport) -> str

Source code in src/replication/reward_hacking.py
def render_text(self, report: RewardHackingReport) -> str:
    lines: List[str] = []
    lines.extend(box_header("REWARD HACKING DETECTOR"))
    lines.append(f"  Generated: {report.generated_at}")
    lines.append(f"  Agents analysed: {report.summary.get('total_agents', 0)}")
    lines.append(f"  Agents flagged:  {report.summary.get('agents_flagged', 0)}")
    lines.append(f"  Total signals:   {report.summary.get('total_signals', 0)}")
    lines.append("")

    if report.signals:
        lines.extend(box_header("SIGNALS"))
        for s in report.signals:
            sev_icon = {"low": "🟢", "medium": "🟡", "high": "🟠", "critical": "🔴"}.get(s.severity.value, "⚪")
            lines.append(f"  {sev_icon} [{s.severity.value.upper():>8}] {s.pattern.value}")
            lines.append(f"    Agent: {s.agent_id}  |  Confidence: {s.confidence:.0%}")
            lines.append(f"    {s.description}")
            lines.append("")

    # Per-agent risk
    lines.extend(box_header("AGENT RISK SCORES"))
    for aid, prof in sorted(report.profiles.items(), key=lambda x: x[1].risk_score, reverse=True):
        bar_len = int(prof.risk_score * 20)
        bar = "█" * bar_len + "░" * (20 - bar_len)
        lines.append(f"  {aid:<20} [{bar}] {prof.risk_score:.0%}")
    lines.append("")

    # Recommendations
    lines.extend(box_header("RECOMMENDATIONS"))
    for i, rec in enumerate(report.recommendations, 1):
        lines.append(f"  {i}. {rec}")
    lines.append("")
    return "\n".join(lines)

render_html(report: RewardHackingReport) -> str

Source code in src/replication/reward_hacking.py
    def render_html(self, report: RewardHackingReport) -> str:
        esc = _html.escape

        signal_rows = ""
        for s in report.signals:
            color = {"low": "#4caf50", "medium": "#ff9800", "high": "#f44336", "critical": "#b71c1c"}.get(s.severity.value, "#999")
            signal_rows += f"""<tr>
                <td style="color:{color};font-weight:bold">{esc(s.severity.value.upper())}</td>
                <td>{esc(s.pattern.value)}</td>
                <td>{esc(s.agent_id)}</td>
                <td>{s.confidence:.0%}</td>
                <td>{esc(s.description)}</td>
            </tr>"""

        risk_bars = ""
        for aid, prof in sorted(report.profiles.items(), key=lambda x: x[1].risk_score, reverse=True):
            pct = prof.risk_score * 100
            color = "#4caf50" if pct < 30 else "#ff9800" if pct < 60 else "#f44336"
            risk_bars += f"""<div style="margin:4px 0">
                <span style="display:inline-block;width:140px">{esc(aid)}</span>
                <div style="display:inline-block;width:200px;height:18px;background:#333;border-radius:3px;vertical-align:middle">
                    <div style="width:{pct:.0f}%;height:100%;background:{color};border-radius:3px"></div>
                </div>
                <span style="margin-left:8px">{pct:.0f}%</span>
            </div>"""

        recs_html = "".join(f"<li>{esc(r)}</li>" for r in report.recommendations)

        # Canvas chart data for metric divergence
        chart_js = ""
        for aid, prof in report.profiles.items():
            for name in prof.metric_names():
                vals = prof.metric_values(name)
                gts = [g for g in prof.ground_truths(name) if g is not None]
                if gts:
                    chart_js += f"""
                    drawChart('{esc(aid)}{esc(name)}',
                        {json.dumps(vals[:50])}, {json.dumps(gts[:50])});"""

        return f"""<!DOCTYPE html>
<html lang="en"><head><meta charset="utf-8">
<title>Reward Hacking Report</title>
<style>
body{{font-family:system-ui,sans-serif;background:#1a1a2e;color:#e0e0e0;margin:20px;}}
h1{{color:#e94560;}} h2{{color:#ff9800;border-bottom:1px solid #333;padding-bottom:4px;}}
table{{border-collapse:collapse;width:100%;margin:10px 0;}}
th,td{{border:1px solid #333;padding:6px 10px;text-align:left;}}
th{{background:#16213e;}} tr:nth-child(even){{background:#16213e33;}}
.card{{background:#16213e;border-radius:8px;padding:16px;margin:12px 0;}}
canvas{{background:#0f3460;border-radius:4px;margin:8px;}}
li{{margin:4px 0;}}
</style></head><body>
<h1>🎯 Reward Hacking Detector</h1>
<p>Generated: {esc(report.generated_at)}</p>
<div style="display:flex;gap:16px;flex-wrap:wrap;">
    <div class="card"><h3>Agents</h3><div style="font-size:2em">{report.summary.get('total_agents',0)}</div>analysed</div>
    <div class="card"><h3>Flagged</h3><div style="font-size:2em;color:#f44336">{report.summary.get('agents_flagged',0)}</div>agents</div>
    <div class="card"><h3>Signals</h3><div style="font-size:2em;color:#ff9800">{report.summary.get('total_signals',0)}</div>detected</div>
    <div class="card"><h3>Avg Confidence</h3><div style="font-size:2em">{report.summary.get('avg_confidence',0):.0%}</div></div>
</div>

<h2>Signals</h2>
<table><tr><th>Severity</th><th>Pattern</th><th>Agent</th><th>Confidence</th><th>Description</th></tr>
{signal_rows}</table>

<h2>Agent Risk Scores</h2>
<div class="card">{risk_bars}</div>

<h2>Metric vs Ground Truth</h2>
<div id="charts"></div>

<h2>Recommendations</h2>
<ul>{recs_html}</ul>

<script>
function drawChart(title, metric, gt) {{
    const div = document.getElementById('charts');
    const c = document.createElement('canvas');
    c.width = 400; c.height = 200;
    div.appendChild(c);
    const ctx = c.getContext('2d');
    const n = Math.max(metric.length, gt.length);
    const all = metric.concat(gt);
    const mn = Math.min(...all), mx = Math.max(...all);
    const range = mx - mn || 1;
    ctx.fillStyle = '#e0e0e0'; ctx.font = '11px sans-serif';
    ctx.fillText(title, 8, 14);
    function y(v) {{ return 180 - ((v - mn) / range) * 160; }}
    function x(i) {{ return 10 + (i / Math.max(n - 1, 1)) * 380; }}
    // metric line
    ctx.strokeStyle = '#e94560'; ctx.lineWidth = 2; ctx.beginPath();
    metric.forEach((v, i) => {{ i === 0 ? ctx.moveTo(x(i), y(v)) : ctx.lineTo(x(i), y(v)); }});
    ctx.stroke();
    // gt line
    ctx.strokeStyle = '#4caf50'; ctx.lineWidth = 2; ctx.beginPath();
    gt.forEach((v, i) => {{ i === 0 ? ctx.moveTo(x(i), y(v)) : ctx.lineTo(x(i), y(v)); }});
    ctx.stroke();
    // legend
    ctx.fillStyle = '#e94560'; ctx.fillText('● Metric', 280, 14);
    ctx.fillStyle = '#4caf50'; ctx.fillText('● Ground Truth', 340, 14);
}}
{chart_js}
</script>
</body></html>"""

render_json(report: RewardHackingReport) -> str

Source code in src/replication/reward_hacking.py
def render_json(self, report: RewardHackingReport) -> str:
    return json.dumps({
        "generated_at": report.generated_at,
        "summary": report.summary,
        "signals": [
            {"pattern": s.pattern.value, "agent_id": s.agent_id,
             "severity": s.severity.value, "confidence": s.confidence,
             "description": s.description, "evidence": s.evidence}
            for s in report.signals
        ],
        "agent_risks": {aid: prof.risk_score for aid, prof in report.profiles.items()},
        "recommendations": report.recommendations,
    }, indent=2)

Detection Details

Metric–Objective Divergence

Compares sliding-window trends of the proxy metric against the ground-truth objective. When the proxy's slope significantly exceeds the ground-truth slope, the agent is likely gaming the metric.

proxy_trend  = 0.05/step  →  improving fast
truth_trend  = 0.01/step  →  barely moving
divergence   = 0.04       →  FLAG: metric diverging from objective

Goodhart Drift

Computes Pearson correlation between proxy and ground-truth in rolling windows. A decreasing correlation signals that the metric is becoming less meaningful — classic Goodhart's Law.

Multi-Metric Inconsistency

When multiple proxy metrics are tracked, checks that correlated metrics move together. If "accuracy" improves but "precision" and "recall" don't, the agent may be exploiting a scoring loophole.