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Cascaded Gaps: Towards Logarithmic Regret for Risk-Sensitive Reinforcement Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace gap-independent analysis with cascaded-gap (gap-dependent) analysis for RSVI2 and RSQ2 | RSVI2 and RSQ2 under entropic risk · episodic finite-horizon tabular MDP | regret scaling in K | Helped |
| Use the risk-dependent normalization factor ψβ in the cascaded gap instead of sign(β) | cascaded gap definition · risk-sensitive MDP with rewards 1 except sub-optimal final-step actions | magnitude consistency of gap across signs of β | Helped |
| Small risk regime |β| ≤ 1/H versus large risk | regret bounds for RSVI2 and RSQ2 · episodic risk-sensitive MDP | regret bound dependence on β | Helped |
| Large risk (|β|(H−1) large) leads to exponential dependence on |β|H in upper and lower bounds | gap-dependent regret · episodic risk-sensitive MDP | regret bound exponential factor | Hurt |
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