entrenar/optim/dp/
accountant.rs

1//! RDP (Renyi Differential Privacy) accountant.
2//!
3//! Provides tighter privacy bounds than basic composition.
4//! Based on Mironov (2017).
5
6use serde::{Deserialize, Serialize};
7
8/// RDP (Renyi Differential Privacy) accountant
9///
10/// Provides tighter privacy bounds than basic composition.
11/// Based on Mironov (2017).
12#[derive(Debug, Clone, Serialize, Deserialize)]
13pub struct RdpAccountant {
14    /// RDP orders to track
15    orders: Vec<f64>,
16    /// Accumulated RDP values for each order
17    pub(crate) rdp: Vec<f64>,
18    /// Number of steps taken
19    steps: usize,
20}
21
22impl RdpAccountant {
23    /// Create a new RDP accountant
24    pub fn new() -> Self {
25        // Standard orders for RDP accounting
26        let orders: Vec<f64> = (2..=256).map(f64::from).collect();
27        let rdp = vec![0.0; orders.len()];
28        Self { orders, rdp, steps: 0 }
29    }
30
31    /// Create with custom orders
32    pub fn with_orders(orders: Vec<f64>) -> Self {
33        let rdp = vec![0.0; orders.len()];
34        Self { orders, rdp, steps: 0 }
35    }
36
37    /// Record a training step
38    pub fn step(&mut self, noise_multiplier: f64, sample_rate: f64) {
39        for (i, &alpha) in self.orders.iter().enumerate() {
40            let rdp_step = compute_rdp_gaussian(noise_multiplier, sample_rate, alpha);
41            self.rdp[i] += rdp_step;
42        }
43        self.steps += 1;
44    }
45
46    /// Get privacy spent as (epsilon, delta)
47    pub fn get_privacy_spent(&self, delta: f64) -> (f64, f64) {
48        rdp_to_dp(&self.orders, &self.rdp, delta)
49    }
50
51    /// Get number of steps
52    pub fn n_steps(&self) -> usize {
53        self.steps
54    }
55
56    /// Reset the accountant
57    pub fn reset(&mut self) {
58        for r in &mut self.rdp {
59            *r = 0.0;
60        }
61        self.steps = 0;
62    }
63}
64
65impl Default for RdpAccountant {
66    fn default() -> Self {
67        Self::new()
68    }
69}
70
71/// Compute RDP of Gaussian mechanism for subsampled data
72pub fn compute_rdp_gaussian(noise_multiplier: f64, sample_rate: f64, alpha: f64) -> f64 {
73    if noise_multiplier <= 0.0 || sample_rate <= 0.0 {
74        return f64::INFINITY;
75    }
76
77    // RDP of Gaussian mechanism: alpha / (2 * sigma^2)
78    // For subsampled mechanism, we use Poisson subsampling bound
79    let sigma = noise_multiplier;
80
81    if sample_rate >= 1.0 {
82        // Full batch
83        alpha / (2.0 * sigma.powi(2))
84    } else {
85        // Subsampled: upper bound using privacy amplification
86        // Simplified bound: q^2 * alpha / (2 * sigma^2)
87        // where q is the sampling rate
88        let q = sample_rate;
89
90        // More accurate bound using log1p for numerical stability
91        if alpha <= 1.0 {
92            return f64::INFINITY;
93        }
94
95        // Approximate subsampled RDP
96        let log_a = (alpha - 1.0) * ((alpha * q.powi(2)) / (2.0 * sigma.powi(2))).min(1.0).ln_1p();
97        log_a / (alpha - 1.0)
98    }
99}
100
101/// Convert RDP to (epsilon, delta)-DP
102pub fn rdp_to_dp(orders: &[f64], rdp: &[f64], delta: f64) -> (f64, f64) {
103    if delta <= 0.0 || orders.is_empty() {
104        return (f64::INFINITY, delta);
105    }
106
107    let log_delta = delta.max(f64::MIN_POSITIVE).ln();
108
109    // Find optimal order
110    let mut min_epsilon = f64::INFINITY;
111    for (&alpha, &rdp_alpha) in orders.iter().zip(rdp.iter()) {
112        if alpha <= 1.0 {
113            continue;
114        }
115        // epsilon = rdp_alpha - (log(delta) + log(alpha - 1)) / (alpha - 1) + log(alpha / (alpha - 1))
116        let epsilon = rdp_alpha
117            + (1.0 / (alpha - 1.0)) * ((alpha - 1.0) / alpha).max(f64::MIN_POSITIVE).ln()
118            - (log_delta + (alpha - 1.0).max(f64::MIN_POSITIVE).ln()) / (alpha - 1.0);
119
120        if epsilon < min_epsilon && epsilon >= 0.0 {
121            min_epsilon = epsilon;
122        }
123    }
124
125    (min_epsilon, delta)
126}
entrenar/optim/dp/accountant.rs

entrenar/optim/dp/
accountant.rs
