File size: 1,304 Bytes
ea3a71e | 1 2 3 4 5 6 7 8 9 | [
"Theorem 5.1 gives the first convergence bound for Federated DPO (FedDPO) under partial client participation, showing gradient-norm error scaling with local steps E, rounds R, sampled clients S, and gradient variance ζ²_g (Theorem 5.1).",
"Corollary 5.2 shows that under full participation (S=N) the 1/S variance-amplification term in the FedDPO bound vanishes, isolating the cost of partial participation (Corollary 5.2).",
"Theorem 5.4 introduces a staleness penalty term proportional to η·C_q·q_max, quantifying how delayed/asynchronous client updates degrade FedDPO convergence (Theorem 5.4).",
"Theorem 5.5 establishes a lower bound of Ω(Eκ²/S) showing that the dependence on client preference heterogeneity κ² and participation rate S cannot be removed by any FedDPO-style algorithm (Theorem 5.5).",
"Theorem 6.1 proves DecDPO (decentralized DPO) converges at rate O(1/√R + 1/(R(1−ρ²))) where ρ is the spectral gap of the communication graph, with variance and heterogeneity terms scaled by 1/(1−ρ²) (Theorem 6.1).",
"Numerical experiments on the Stanford Human Preferences dataset with N=5 agents empirically confirm the predicted effects of local step count, participation rate, staleness, and network topology on convergence (Section 7, Numerical Results)."
]
|