financial algorithm developers

Abstract: A central topic in online and stochastic optimization is to design algorithms that do not require tuning of hyperparameters. Successful strategies in online learning include AdaGrad-style learning rates, Conic Blackwell algorithms, and parameter-free algorithms. However, these classes require different, often difficult, analyses. We develop a unifying family of Online Convex Optimization (OCO) algorithms that require no user-tuned learning rate on convex domains that may be unbounded. The construction lifts the domain to a cone by adding one scalar coordinate, an idea going back to Blackwell (1954). The lifted subgradients are orthogonal to the corresponding lifted decisions, leaving the comparator scale free to optimize in the regret analysis. Applying Follow-the-Regularized-Leader (FTRL) and Online Mirror Descent (OMD) on the cone recovers Conic Blackwell Algorithm (CBA) and Conic Blackwell Algorithm Plus (CBA$^+$) on bounded domains in Hilbert spaces and extends them to finite-dimensional normed spaces with a strongly convex squared norm. For arbitrary nonempty closed convex domains in these spaces, a known gradient bound yields parameter-free regret guarantees. Surprisingly, on an unconstrained Hilbert space, the construction recovers the Krichevsky--Trofimov (KT) coin-betting algorithm exactly. We also give a parameter-free algorithm for unconstrained domains that requires no gradient bound.

Abstract: Automated agentic-system design is typically evaluated on static task suites with immediate scalar rewards. Deployed systems face persistent shift, delayed dependent feedback, correlated component failures, and costly architecture changes. We formalize meta-agent architecture search as sequential incumbent replacement with switching costs and hard risk constraints and introduce Conservative Meta-Agent Search (CMAS). CMAS retrieves archived architectures and proposes typed graph edits, then scores each against the incumbent by paired shadow replay under common random numbers, with interventional component credit. Promotion requires an empirically calibrated, variance-penalized simultaneous score above a pre-specified margin, and is followed by a simulated canary stage and pre-specified rollback. Since backtests cannot certify meta-level skill, we introduce MetaInvest-Bench, a regime-switching simulator whose specified worker competence makes a surrogate-optimal architecture computable, with leakage-controlled replay, adversarial governance tracks, and five negative controls. Financial streams serve as a risk-sensitive testbed for meta-level generalization; we claim no alpha. Across 96 streams, CMAS cuts normalized mean surrogate dynamic-oracle regret from 0.116 to 0.104 and raises held-out utility from 0.44 to 0.48 over the strongest adaptive baseline; when extra workers add no value, it contracts to near-single-agent teams. Its deployment inference cost is ~6% lower, though its search-inclusive token cost is the highest of the methods compared. The observed per-update false-promotion rate is 3.4% against a nominal 5% target, and 4.8% in a sealed rerun. The calibration is empirical: it concerns an update-level replay statistic on an author-designed benchmark, and guarantees neither full-utility improvement, nor absence of simulated canary-stage harm, nor sequence-level error control.

Abstract: Language-model agents are increasingly asked to run experiments, yet benchmarks rarely measure whether those experiments improve the decisions they are meant to inform. We introduce CrashGym, a deterministic, replayable limit-order-book simulator in which an agent must choose between a deleveraging intervention and a liquidity backstop for a market about to suffer a shock-triggered crash. Before committing, the agent may query intervention experiments in a laboratory realization of the market. Its choice is then scored on an independently seeded target realization in which the simulator executes every feasible intervention, so regret relative to the best intervention is computed by directly simulating every alternative on the same target repeats, with no human or model-based judging. The simulator implements each amplification channel---persistent price impact, liquidity withdrawal, margin-driven liquidation, and an evolving strategy mix---as an explicit mechanism that can be switched on in stages. In a prospectively specified study on 24 newly sampled worlds, laboratory access reduces the mean regret of the one deployment with a complete record (Luna) from 8.878 to 3.785, a paired reduction of 5.092 utility units (nominal 95% world-bootstrap interval: 1.028--9.507), or 57.4% of the OBSERVE-ONLY mean. Prospective comparisons for two further deployments are incomplete; in a separate exploratory study, mean regret is lower with laboratory access for all four deployments evaluated. A laboratory whose strategy mix evolves endogenously yields no established advantage over one with a fixed mix. CrashGym thus measures the value of experimentation as avoided decision loss and lets simulator detail be judged by the decisions it supports.

Abstract: Decisions that weigh several reward signals against each other require the joint distribution of the return vector. Categorical critics scale exponentially in the reward dimension, and quantiles have no canonical multivariate analogue. Multivariate distributional critics therefore represent each return distribution by M equal-weight particles trained with a discrepancy loss. Beyond their atoms, the particles provide no sampler and cannot resolve events rarer than 1/M. We propose Stein variational distributional RL (SVDRL). Its critic outputs Stein particles, which Stein variational gradient descent transports along a learned score field of the distributional Bellman target. We learn this field by bootstrapped denoising score matching across noise levels and tie it across the Bellman recursion by a consistency loss, which we prove is a non-expansive temporal-difference scheme in score space. The same field certifies the particles. Its reverse-diffusion sampler satisfies a supremal Wasserstein policy-evaluation bound that holds for bounded, possibly multimodal returns. The Stein particles inherit this bound up to a gap that we measure without ground truth, and the sampler answers tail-risk queries below the particle resolution at any sample size. Empirically, SVDRL is more accurate on rare events than particle critics with the same number of particles, and on par on MuJoCo continuous control.

Abstract: Reinforcement learning (RL) is increasingly used for financial optimal-control problems when complex dynamics make analytical strategies difficult to obtain. There are financial mathematics literactures which provides many solved models whose equations and controls could evaluate and guide learning; we ask whether RL can exploit these results. We place a proximal policy optimisation (PPO) agent in an analytically solved continuous-time broker--trader game. PPO replaces the broker and chooses its trading speed while interacting with an informed trader and stochastic uninformed order flow. We derive a finite-step reward from the broker's continuous-time payoff and verify its discrete implementation through grid refinement and an exact one-step identity. With zero uninformed flow, a validation-selected PPO--FFNN approaches the reference action. With stochastic uninformed flow, the tested PPO--FFNN and PPO--LSTM remain inaccurate, although supervised learning confirms that their actors can represent the action. Monte Carlo diagnostics show that their critics do not reliably rank nearby actions; potential-based reward shaping also gives no reliable improvement. Under partial information, a causal certainty-equivalent controller based on the broker's observable history remains close to the reference, while PPO has larger errors and lower payoffs. Finally, we freeze the analytical policy and train PPO to adjust it after the execution cost changes. Halving the cost yields a repeatable improvement that closes \(2.22\%\) of the gap to the changed-cost reference. The analytical solution therefore provides both a benchmark for diagnosing RL and a useful starting policy for adaptation.

Abstract: When developers change one component of an agent, such as its controller, a learned model or its verifier, they usually judge the change by an aggregate task score. That score cannot tell whether improvement was attainable, which component lost value, or what the agent's own checks certify. We introduce a claim-specific verification audit for modular agents that plan, act, check and refine. Instead of scoring the agent, the audit scores the evidence: each conclusion is recorded with the evidence behind it, one of four verdicts (supported, unsupported, unresolved or not evaluated) and the boundary within which it holds. Three tools supply that evidence. Oracle policies measure attainable improvement under an explicitly stated action set, so that a low value can be traced to the evaluation rather than to the environment. Replacing one component at a time with a perfect counterpart locates lost value, with null results read as unresolved whenever a downstream component could mask them. A separate test asks whether the verifier's score identifies the quantity it is read as bounding. Applied to a constrained portfolio-allocation agent in a synthetic market with known hidden regimes, the audit shows that the value of perfect regime information depends on the action set used to measure it, that the scenario generator discards most of the regime signal while better local fidelity does not improve decisions, and that the runtime verifier can be bypassed with no visible change in outcomes. The contribution is the protocol and the evidential distinctions it enforces; the empirical findings are specific to the agent and environment studied.

Abstract: Non-stationary online learning has attracted much attention in recent years, as static regret is insufficient to guide algorithm design in changing environments. To address this limitation, interval regret and dynamic regret have been introduced as two representative performance metrics that strengthen static regret in complementary directions. Interval regret requires an online algorithm to achieve competitive static regret over every local time interval, whereas dynamic regret evaluates performance against an arbitrary sequence of time-varying comparators. Despite their importance, the relation between these metrics has long remained unclear. Prior work has often regarded interval regret as the stronger notion, based on the intuition that local guarantees should naturally induce global guarantees. Consequently, it is widely conjectured that an algorithm with optimal interval regret should automatically attain optimal dynamic regret. In this paper, we first establish a negative result that refutes this intuition of a metric-level implication. Specifically, for both convex and curved functions (including exp-concave and strongly convex functions), we show that there exist instances in which an algorithm with optimal interval regret nevertheless fails to achieve optimal dynamic regret. We then show how to leverage local adaptivity to obtain optimal dynamic regret. In particular, optimal dynamic regret can be attained by invoking an interval regret minimization process over an enlarged Euclidean ball containing the original convex feasible domain and using a suitable domain-converted surrogate loss. This reduction applies to both convex and curved functions. As a byproduct, we obtain the first proper and efficient algorithm with optimal dynamic regret for exp-concave functions, improving prior results while significantly simplifying the analysis.

Abstract: Many real-world reinforcement learning (RL) problems evolve in continuous time, where decisions occur at irregular, event-driven intervals rather than at fixed discrete steps. We study episodic continuous-time Markov Decision Processes (MDPs) in which decision epochs are governed by a homogeneous Poisson process and the reward and transition dynamics vary smoothly over time. We consider both a fixed number of jumps per episode and a fixed time budget with a random number of Poisson decision epochs. Under a Lipschitz continuity assumption in time, we exploit local smoothness through discretization and extend both UCRL (Auer and Ortner 2006) and Q-learning (Jin et al. 2018) to this setting, proving $\widetilde{O}(T^{2/3})$ regret bounds for both model-based and model-free algorithms. Finally, we establish matching $\widetildeΩ(T^{2/3})$ minimax lower bounds, showing that the rate is optimal up to logarithmic factors. These results provide the first tight regret guarantees for Lipschitz-smooth continuous-time episodic MDPs with Poisson decision epochs.

Abstract: We consider an agent acting against a general non-Markovian environment. The agent maintains its agent states, but is free to choose a transition kernel across those states and optimize its state-feedback control policies. We study the bi-level agent design problem that optimizes the transition kernel and the policy it induces, given said kernel with offline data of observations and actions obtained via a behavioral policy. For general environments, we show that a soft $Q$-learning algorithm converges almost surely to the fixed point of a soft Bellman equation defined by the stationary averages that the behavioral policy and the chosen kernel induce, and we delineate what separates the resulting policy from an optimal one. In partially observed Markov decision problems, we analyze convergence properties of parametrized transition kernel design via zero-th order and Bayesian optimization techniques.