Research map / Optimization / Nonconvex and smooth optimization
Efficient Regret Minimization in Non-Convex Games
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a time-smoothed local-regret objective instead of standard global regret | Non-convex online optimization · Non-convex online optimization | w-local regret: \mathfrak{R}_w(T) \leq \pa{\delta + 2L}^2 \frac{T}{w^2} | Helped |
| Use a window-smoothed performance measure | Any online algorithm under adversarial losses · Adversarial non-convex online optimization | expected w-local regret lower bound: \E_\mathcal{D} \bra{ \mathfrak{R}_w(T) } \geq \frac{1}{4w} \left\lfloor \frac{T}{2w} \right\rfloor | Mixed |
| Average stochastic gradients across a window of size w | Time-smoothed online gradient descent · Non-convex optimization with stochastic gradients | expected w-local regret: \mathbb{E}\left[\mathfrak{R}_w(T)\right] \leq \pa{ 8\beta M + \sigma^2 } \frac{ T }{ w } | Helped |
| Replace gradient-descent epochs with second-order Newton and negative-curvature steps | Time-smoothed online gradient descent · Non-convex online optimization with second-order guarantees | sum of second-order stationarity measures: \sum_{t=1}^T \Phi_t(x_t) \leq C_1 \cdot \frac{T}{w^2} | Helped |
| Replace the inner-loop gradient descent with non-convex SVRG | Time-smoothed online gradient descent in the unconstrained case · Unconstrained non-convex online optimization | gradient oracle calls: O(Tw^{5/3}) | Helped |
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