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247 lines
17 KiB
XML
247 lines
17 KiB
XML
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<!-- ========================================================= -->
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<!-- COLUMN 1: THE THREAT (COI & SATURATION) -->
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<!-- ========================================================= -->
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<text x="60" y="80" font-family="Georgia, serif" font-size="28" font-weight="bold" fill="#333333">1. The Vulnerability</text>
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<!-- Top: COI Bell Curve -->
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<g transform="translate(60, 130)">
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Cost of Information from First Principles</text>
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<text x="0" y="70" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">P ~ π(τ)</text>
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<text x="0" y="105" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B"><tspan text-decoration="underline">p</tspan> = reservation price</text>
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<text x="0" y="140" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">M = P - <tspan text-decoration="underline">p</tspan></text>
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<!-- Bell Curve -->
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<!-- Markers p and E[P] -->
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<text x="150" y="375" font-family="Georgia" font-style="italic" font-size="22" fill="#E37862" text-anchor="middle"><tspan text-decoration="underline">p</tspan></text>
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<text x="260" y="375" font-family="Georgia" font-style="italic" font-size="22" fill="#85B589" text-anchor="middle">E[P]</text>
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<!-- COI Annotation -->
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<text x="310" y="138" font-size="16" fill="#E37862" text-anchor="middle">average information rent</text>
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<text x="310" y="118" font-family="Georgia" font-style="italic" font-size="22" fill="#E37862" font-weight="bold" text-anchor="middle">COI = E[P] - <tspan text-decoration="underline">p</tspan></text>
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</g>
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<!-- Bottom: Agent Saturation -->
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<g transform="translate(60, 580)">
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Why COI Erodes with Agent Saturation</text>
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<text x="0" y="75" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">p<tspan font-size="14" dy="5">(1)</tspan><tspan dy="-5"> = min(p</tspan><tspan font-size="14" dy="5">1</tspan><tspan dy="-5">, ..., p</tspan><tspan font-size="14" dy="5">N</tspan><tspan dy="-5">)</tspan></text>
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<text x="0" y="115" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">P(p<tspan font-size="14" dy="5">(1)</tspan><tspan dy="-5"> > t) = [1 - F(t)]</tspan><tspan font-size="14" dy="-10">N</tspan></text>
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<!-- Erosion Graph -->
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<line x1="140" y1="350" x2="140" y2="170" stroke="#333" stroke-width="2"/>
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<text x="260" y="375" font-size="16" font-style="italic" fill="#555" text-anchor="middle">F(t)</text>
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<text x="120" y="260" font-size="16" font-style="italic" fill="#555" text-anchor="middle" transform="rotate(-90 120 260)">[1 - F(t)]^N</text>
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<!-- Curves -->
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<text x="390" y="220" font-size="16" fill="#4EA5D9" font-weight="bold">N=1</text>
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<text x="390" y="250" font-size="16" fill="#85B589" font-weight="bold">N=4</text>
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<text x="390" y="280" font-size="16" fill="#E37862" font-weight="bold">N=16</text>
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<text x="260" y="420" font-size="20" fill="#555" text-anchor="middle">As independent query count grows,</text>
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<text x="260" y="445" font-size="20" fill="#E37862" font-weight="bold" text-anchor="middle">realizable markup collapses.</text>
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</g>
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<!-- ========================================================= -->
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<!-- COLUMN 2: THE BEHAVIORAL SIGNAL -->
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<!-- ========================================================= -->
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<text x="700" y="80" font-family="Georgia, serif" font-size="28" font-weight="bold" fill="#333333">2. The Behavioral Signals</text>
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<!-- Top: Transition Kernels -->
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">From Session Paths to Transition Kernels</text>
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<text x="0" y="75" font-size="20" fill="#85B589" font-weight="bold">human: start → view → detail → cart → purchase</text>
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<text x="0" y="115" font-size="20" fill="#E37862" font-weight="bold">agent: start → view → detail → view → detail</text>
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<text x="0" y="170" font-family="Georgia, serif" font-style="italic" font-size="24" fill="#8C7A6B">
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P̂(s'|s) = <tspan font-size="18" dy="-12">N(s,s')</tspan> / <tspan font-size="18" dy="12">Σ N(s,k)</tspan>
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</text>
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<!-- Matrix Representation -->
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<text x="125" y="250" font-size="16" fill="#4EA5D9" text-anchor="middle">transition counts N(s,s')</text>
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<text x="375" y="250" font-size="16" fill="#85B589" text-anchor="middle">normalized kernel T</text>
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<!-- Arrow -->
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<!-- Matrix 2 -->
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<text x="80" y="110" font-family="monospace" font-size="14" fill="#333" text-anchor="middle" textLength="142" lengthAdjust="spacingAndGlyphs">0.00 0.14 0.00 0.86</text>
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<text x="250" y="440" font-size="18" fill="#777" text-anchor="middle">Kernel shape is the compact behavioral signature used downstream.</text>
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</g>
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<!-- Bottom: Separability Distributions -->
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<g transform="translate(700, 600)">
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Separability into a Control Signal</text>
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<text x="0" y="75" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">Δ<tspan font-size="16" dy="5">H</tspan><tspan dy="-5"> = D</tspan><tspan font-size="16" dy="5">KL</tspan><tspan dy="-5">(T̂' || T̄</tspan><tspan font-size="16" dy="5">H</tspan><tspan dy="-5">)</tspan></text>
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<text x="0" y="115" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">Δ<tspan font-size="16" dy="5">A</tspan><tspan dy="-5"> = D</tspan><tspan font-size="16" dy="5">KL</tspan><tspan dy="-5">(T̂' || T̄</tspan><tspan font-size="16" dy="5">A</tspan><tspan dy="-5">)</tspan></text>
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<text x="0" y="155" font-family="Georgia, serif" font-style="italic" font-size="24" fill="#8C7A6B">g = Δ<tspan font-size="16" dy="5">H</tspan><tspan dy="-5"> - Δ</tspan><tspan font-size="16" dy="5">A</tspan></text>
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<!-- Curves -->
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<text x="180" y="235" font-family="Georgia, serif" font-style="italic" font-size="22" text-anchor="middle">g = Δ<tspan font-size="16" dy="5">H</tspan><tspan dy="-5"> - Δ</tspan><tspan font-size="16" dy="5">A</tspan></text>
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<!-- Human Curve -->
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<text x="70" y="110" font-size="22" fill="#4EA5D9" font-weight="bold">human</text>
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<!-- Agent Curve -->
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<text x="290" y="110" font-size="22" fill="#E37862" font-weight="bold">agent</text>
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<!-- Decision Boundary -->
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<text x="180" y="-5" font-size="16" fill="#777" text-anchor="middle">decision boundary</text>
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<text x="210" y="180" font-family="Georgia" font-style="italic" font-size="20" fill="#ECA233" text-anchor="middle">g_obs</text>
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<text x="180" y="280" font-size="18" fill="#555" text-anchor="middle">Positive gap shifts score toward agent traffic.</text>
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</g>
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</g>
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<!-- ========================================================= -->
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<!-- COLUMN 3: THE SOLUTION (CONTAMINATION & DR-RL) -->
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<!-- ========================================================= -->
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<text x="1340" y="80" font-family="Georgia, serif" font-size="28" font-weight="bold" fill="#333333">3. Robust Control & Contamination</text>
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<!-- Top: Contamination Generator -->
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Contamination Generator G(α)</text>
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<!-- Boxes -->
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<text x="120" y="100" font-size="18" fill="#222" text-anchor="middle">labeled human sessions</text>
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<text x="380" y="100" font-size="18" fill="#222" text-anchor="middle">synthetic agent sessions</text>
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<!-- Mixed Batch -->
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<text x="250" y="220" font-size="18" fill="#222" text-anchor="middle">mixed batch for training</text>
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<!-- Alpha Bar -->
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<text x="250" y="275" font-family="Georgia, serif" font-size="20" fill="#555" text-anchor="middle">alpha = 0.33</text>
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<text x="184" y="340" font-size="18" fill="#4EA5D9" text-anchor="middle">human share (1-α)</text>
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<text x="384" y="340" font-size="18" fill="#E37862" text-anchor="middle">agent share (α)</text>
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<!-- Bottom: Distributionally Robust Control -->
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<text x="0" y="30" font-size="24" font-weight="bold" fill="#444">Distributionally Robust Control Layer</text>
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<text x="0" y="80" font-family="Georgia, serif" font-style="italic" font-size="22" fill="#8C7A6B">
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π* = arg max<tspan font-size="16" dy="5">π</tspan> min<tspan font-size="16" dy="0">Q ∈ U<tspan font-size="12" dy="5">ε</tspan></tspan>
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<tspan dy="-10"> E</tspan><tspan font-size="16" dy="5">d ~ Q</tspan>
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<tspan dy="-5">[ R(p,d) - λ COI</tspan><tspan font-size="16" dy="5">leak</tspan><tspan dy="-5">(p,τ') ]</tspan>
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</text>
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<!-- Ambiguity Ball -->
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<text x="-95" y="-120" font-family="Georgia" font-style="italic" font-size="24" fill="#C4A45B">U<tspan font-size="16" dy="5">ε</tspan></text>
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<!-- Points -->
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<circle cx="0" cy="0" r="7" fill="#4EA5D9"/>
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<text x="12" y="24" font-family="Georgia" font-style="italic" font-size="22" fill="#4EA5D9">P̂<tspan font-size="14" dy="5">N</tspan></text>
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<text x="-140" y="-50" font-family="Georgia" font-style="italic" font-size="18" fill="#E37862">worst-case Q*</text>
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<circle cx="70" cy="50" r="6" fill="#85B589"/>
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<!-- Process Steps -->
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<text x="110" y="28" font-size="16" fill="#E37862" font-weight="bold" text-anchor="middle">inner min picks Q*</text>
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<text x="110" y="123" font-size="16" fill="#9E8033" font-weight="bold" text-anchor="middle">sample demand from Q*</text>
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<text x="250" y="440" font-size="18" fill="#555" text-anchor="middle">Reward is evaluated on demand drawn from Q*, then used for the policy step.</text>
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</svg>
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