Optimization Is Not All You Need

Prompt optimization in compound AI systems is statistically indistinguishable from a coin flip: across 72 optimization runs on Claude Haiku 4.5 (6 methods $\times$ 4 tasks $\times$ 3 repeats), 49% score below zero-shot; on Amazon Nova Lite, the failure rate is even higher. Yet on one task, all six methods improve over zero-shot by up to $+6.8$ points. What distinguishes success from failure? We investigate with 18,000 grid evaluations and 144 optimization runs, testing two assumptions behind end-to-end optimization tools like TextGrad and DSPy, in the order they must be answered: (A) agent prompts interact, requiring joint rather than independent optimization, and (B) individual prompts are worth optimizing at all. Interaction effects are never significant ($p > 0.52$, all $F < 1.0$), and optimization helps only when the task has exploitable output structure: a format the model can produce but does not default to. We further give a mechanistic account: instruction-tuning compresses input phrasing into a narrow output distribution, eliminating the very phrasing-sensitivity that joint optimization assumes. We provide a two-stage diagnostic: an $80 ANOVA pre-test for agent coupling, and a 10-minute headroom test that predicts whether optimization is worthwhile, turning a coin flip into an informed decision.

Automated prompt optimization methods (e.g., DSpy, TextGrad) can substantially improve the performance of large language model (LLM), however, their generalization ability across different tasks remains underperformed. In practice, the superiority of the optimized prompt on one benchmark often fails to transfer to another, and this limitation persists even when switching across different LLM backbones. To investigate the underexplored sources of heterogeneity in prompt performance, we conduct a causal inference-inspired observational analysis of optimized prompts across a diverse set of optimization frameworks, LLM backbones, and NLP benchmarks. To achieve the goal, we build upon the propensity-adjusted associational analysis together with multiple complementary representations of prompt edits, where the consistent task-conditioned edits patterns are identified. We find that complexity-increasing and meta-instructional edits are negatively associated with mathematical and multi-hop reasoning performance, whereas step-by-step and meta-cognitive edits improve logical and sequential reasoning tasks. These effects are robust across cognitive-load annotations, surface-level text features, and edit-motif analyses, and can generalize across optimization frameworks. Overall, these results indicate that prompt optimization failures arise from systematic interactions between edit families and task characteristics rather than random optimization artifacts, providing feature-level characterization of optimizer behavior and motivating future task-conditioned optimizer design.

A higher evaluation score does not always mean a better language model system. When optimization exploits an evaluator's mistakes, measured progress can conceal unchanged or deteriorating task performance. This failure can arise through parameter updates, selection among generated outputs, or revisions to persistent prompts. We develop a comparative framework for reward hacking across these three optimization substrates: weights, selection, and text. Building on the Proxy Compression Hypothesis and research on inference-time and in-context reward hacking, we examine how reachable behavior, optimization budgets, and persistent adaptation shape exposure to proxy error. We formalize a distance-dependent upper bound on evaluator disagreement and a capacity ordering for nested policy classes, then show why distance alone cannot establish a universal ranking of vulnerability. An exact finite-output illustration demonstrates how the location of a scoring defect changes the behavior favored by each method. We also map representative defenses across substrates, identifying which mechanisms transfer directly and which offer only functional analogies. Persistent prompts receive particular attention: their contents are inspectable, but the behavior induced by a small textual change may be difficult to anticipate. The formal analysis, numerical illustration, and published evidence together provide a basis for comparing optimization methods and identifying the conditions under which their defenses transfer. The resulting framework connects optimization choices to verification requirements: reliable improvement depends on controlling accessible failure modes and preserving evidence of task quality independent of the score being optimized.