Internalizing Investment Mandates: A Neurosymbolic RL Approach to Portfolio Allocation

Reinforcement-learning portfolio policies can optimize allocations from prices, covariances, and prior positions, yet they lack a calibrated, replayable mechanism for certifying that a proposed allocation respects a bounded risk envelope before execution. Regulators increasingly expect automated portfolio systems to provide exactly this kind of pre-trade audit trail, interpretable risk limit, and human-oversight mechanism. Gated Conformal Semantic Risk Control addresses this gap by separating return-seeking allocation from text-conditioned downside-risk verification. An instruction-tuned language model maps timestamped disclosures into schema-validated semantic risk states over macro, liquidity, earnings, and sector channels. These states induce correlated ellipsoidal factor-shock uncertainty sets whose conformal radii are calibrated by rolling finite-sample prediction over localized semantic nonconformity buckets. An asymmetric second-order cone gate then checks each raw PPO proposal against a certified worst-case semantic loss budget. The gate stays inactive for compliant proposals and intervenes only when that budget is exceeded. In walk-forward out-of-sample tests on nine liquid U.S. Select Sector SPDR ETFs, Raw PPO earns a 12.7% annual return while incurring a 4.05% semantic violation rate. Gated-CSRC removes all observed out-of-sample semantic limit breaches while retaining an 11.7% annual return. This 100-basis-point auditable safety premium is smaller than the yield loss imposed by unconditional hard projection, and exact McNemar testing confirms the compliance gain at $p < 10^{-15}$. Loughran-McDonald lexicon controls and time-shuffled text controls fail to reproduce this certificate.

We study continuous-time mean--variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes, yet the coefficients of these processes are unknown. Based on the recently developed reinforcement learning (RL) theory for diffusion processes, we present a general data-driven RL approach that learns the pre-committed investment strategy directly without attempting to learn or estimate the market coefficients. For multi-stock Black--Scholes markets without factors, we further devise an algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of the Sharpe ratio. We then carry out an extensive empirical study implementing this algorithm to compare its performance and trading characteristics, evaluated under a host of common metrics, with a large number of widely employed portfolio allocation strategies on S&P 500 constituents. The results demonstrate that the proposed continuous-time RL strategy is consistently among the best, especially in a volatile bear market, and decisively outperforms the model-based continuous-time counterparts by significant margins.

Humans carry behaviour knowledge of how to act in familiar situations into every new task rather than relearning it from scratch. There is no reason a Reinforcement Learning (RL) agent shouldn't do the same: known behaviour patterns need not be learned, only applied. Neuro-symbolic RL bridges prior knowledge and RL by injecting symbolic knowledge alongside a learned policy. The point at which this knowledge is integrated is critical: a poor choice can produce, for instance, hallucinated preconditions, which surface as safety and reliability problems in agents acting in changing environments. We formalise this behavioural knowledge as a precondition Bayesian network (BN) over the agent's structural actions - the actions whose legality depends on preconditions, such as picking up a key, grasping a block, toggling a door, or dropping an object. The BN restricts when these actions may fire, and we inject it into the RL loop at three placements: (1) a symbolic verifier, consulted only at inference, that fires a structural action once its preconditions hold; (2) a symbolic enforcer, active during both training and inference, that governs structural-action use throughout learning; and (3) a symbolic learner, which folds the knowledge into the network and learns the restriction and use of structural actions itself. To test the three variants we run experiments on two benchmarks with opposite regimes: one built on long, ordered planning chains, the other on continuous manipulation. We compare against strong baselines on solution quality, sample efficiency, and traceability. The payoff is substantial. On MiniGrid, all three placements improve the solution quality over the PPO+RND baseline, the symbolic enforcer leading at $98.2\%$ against the baseline's $88.8\%$. On Fetch, $\dots$