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Adversarial Causal Bayesian Optimization
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Introduces adversarial causal Bayesian optimization (ACBO) and the CBO-MW algorithm, which combines multiplicative weights with optimistic counterfactual reward estimates from calibrated causal GP models, plus a distributed variant for combinatorial actions.
Problem
Causal Bayesian optimization assumes a stationary system with a single agent, but real systems face external events and other agents that intervene concurrently, so the agent must adapt to adversarial non-stationarity without knowing the mechanisms.
Approach
Combine multiplicative-weights online learning over interventions with optimistic counterfactual reward estimates obtained by propagating GP confidence bounds through the known causal graph, yielding the first bounded-regret algorithm for adversarial CBO; a distributed variant decomposes the action space across per-node agents for submodular rewards.
Key results
- CBO-MW (ACBO) has the strongest or joint-strongest performance on 7 of 8 function network environments, with MCBO and UCB showing linear regret while GP-MW and CBO-MW grow sublinearly.
- Theory gives regret bound O(sqrt(T log|A|) + sqrt(T log(2/delta)) + (B+sqrt(gamma_T+log(m/delta)))^{N+1} d^N L_sigma^N L_f^N m sqrt(T gamma_T)), which can be polynomial in m for binary-tree graphs versus exponential for GP-MW.
- On the SMS rebalancing simulator, the distributed CBO-MW (SUBALG) fulfills more trips over 200 days than D-GP-MW and is significantly more sample efficient, learning demand patterns faster in early rounds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use causal modeling and adversarial adaptation instead of non-adversarial methods | Function network environments · 8 function network environments | regret | Helped |
| use ACBO instead of GP-MW | Function network environments · 7 of 8 function network environments | regret | Helped |
| use ACBO instead of GP-MW | Ackley-Penny · Ackley-Penny | regret | Hurt |
| use a structured causal reward model with multiple low-dimensional GPs instead of a single high-dimensional GP | Distributed ACBO · Shared Mobility System simulator | sample efficiency | Helped |
| use a structured causal reward model with multiple low-dimensional GPs instead of a single high-dimensional GP | Distributed ACBO · Shared Mobility System simulator | total trips | Helped |
Surprising findings
- GP-MW outperforms CBO-MW on Ackley-Penny, which is dense (degree approx. m), consistent with theory that causal structure helps mainly in sparse high-dimensional graphs.
Limitations
- Regret bound can be non-sublinear for Matern kernels when N and c are large due to information gain growth.
- Distributed variant's approximation guarantees require monotone DR-submodular rewards and curvature assumptions.
- Assumes known DAG and calibrated models; the causal UCB oracle is non-convex and solved with random restarts.
Experimental setup
Datasets: Louisville shared mobility trip data (SMS simulator) function networks (Dropwave, Alpine, Rosenbrock, Ackley variants)
Benchmarks: function networks with adversaries (Dropwave, Alpine, Rosenbrock, Ackley with Penny/Perturb) Shared Mobility System rebalancing simulator
Metrics: cumulative regret total trips fulfilled
Baselines: GP-MW UCB MCBO Random D-GP-MW
Builds on: GP-MW MCBO multiplicative weights Exp3 StackelUCB
Closest papers by meaning
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- Robustly Improving Bandit Algorithms with Confounded and Selection Biased Offline Data: A Causal Approach (AAAI 2024 · similarity 0.86)
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